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Last updated date: 19th Sep 2024
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## JEE Advanced Maths Quadratic Equations Important Questions from PYQs with Solutions

 Category: JEE Advanced Important Questions Content-Type: Text, Images, Videos and PDF Exam: JEE Advanced Chapter Name: Quadratic Equations Academic Session: 2024 Medium: English Medium Subject: Mathematics Available Material: Chapter-wise Important Questions with PDF

## Secure a Top Score in Your JEE Advanced Maths Quadratic Equations Exam with Our Practice Papers

Competitive Exams after 12th Science

From 2018, the JEE exam will be conducted in the online mode. The concept of Quadratic equations forms the basis of algebra in the higher class. This chapter has vast applications and can be combined with a lot of other chapters while being questioned in the actual examination. You can expect around 1 to 2 questions from this chapter in the JEE Advanced paper.

The answers given to the Quadratic Equations Important Questions JEE Advanced here are filed with numerous short cut techniques and quick tips. This is very much necessary as the question in the JEE Advanced paper expects to only choose the right answer from the given set of answers. Therefore it is important to have speed and accuracy while solving these sums.

Here is a list of a few important concepts in this chapter based on which questions have been asked repeatedly in the previous year's papers.

• The general form of quadratic equation

• Conditions for nature of roots using discriminant

• Conditions for minimum and maximum value of parabola

• Conditions for minimum and maximum value of a parabola

• The relation between roots and coefficient of the quadratic equation

• The discriminant of quadratic equations.

The quadratic equation is a second-degree equation. It is generally expressed in the form of ax2+bx+c = 0, where a, b, c are real numbers and a ≠ 0. For example, x2+2x+1 = 0. An algebraic expression with multiple terms is called a polynomial. When the quadratic polynomial is equated to zero, it is called a quadratic polynomial.

### Roots of a Quadratic Equation:

If a value of x satisfies the quadratic equation, then they are called roots of the quadratic equation. They are also called zeros of solutions of the equation. An equation can be solved either by the factorisation method where you factorize the equation and equate it to zero or by using the quadratic formula. They both give solutions to the equation.

### Sum and Product of Roots:

If α and β are said to be the roots of the quadratic equation ax2+bx+c = 0,

Then the product of the roots is αβ = c/a

The sum of the roots is α + β = -b/a

### Nature of Roots:

D in quadratic equation denotes discriminant

• If D is equal to 0, the roots of the equation are real and equal.

• If D is greater than 0, the roots of the equation are real and unequal.

• If D is less than 0, the roots of the equation are imaginary and unequal.

• If D is greater than 0 and D is a perfect square, the roots of the equation are rational and unequal.

• If D is greater than 0 and D is not a perfect square, the roots of the equation are irrational and unequal.

### Graph of a Quadratic Equation:

Consider a quadratic equation ax2+bx+c = 0, where a, b, and c are real and

a is not equal to 0. The figure we see on the graph of a quadratic equation is a parabola.

• Case 1: If a>0, D > 0: the graph of the equation is concave upwards and intersects the x-axis at two points. Then the equation will have two real roots. The curve is always above the x-axis

• Case 2: If a>0, D = 0:  the graph of the equation curves upwards and intersects the x-axis at one point. The equation will have two equal roots

• Case 3: If a>0, D < 0: the graph has a curve upwards in a concave shape.  The curve does not intersect the x-axis and the equation has imaginary roots.

• Case 4: If a<0, D>0:  the graph has a curve downwards in a concave shape and intersects the x-axis at two points. The roots of the equation are two real roots.

• Case 5: If a<0, D=0: the parabola is curved downwards and intersects the x-axis at one point. The equation will have two equal roots.

• Case 6: If a<0, D<0: the parabola is concave downwards and does not intersect the x-axis at any point. The equation will have imaginary roots.

## Formulaic Support: Boosting Understanding with  JEE Advanced Quadratic Equations Important Questions

If you're aiming for effective learning, consider employing a strategic approach that integrates Quadratic Equations important questions for JEE Advanced with essential formulas and crucial questions. Formulas serve as concise explanations of fundamental concepts, while solved questions provide a comprehensive learning experience. A strong foundation is established through JEE Advanced Quadratic Equations Important Questions, and formulas aid in comprehending concepts and addressing problems. This fusion streamlines complex topics and enhances memory retention, ultimately boosting your comprehension and academic performance.

• $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

2. Nature of Roots:

• If $b^2 - 4ac > 0$, the roots are real and distinct.

• If $b^2 - 4ac = 0$, the roots are real and equal.

• If $b^2 - 4ac < 0$, the roots are complex conjugates.

3. Sum and Product of Roots:

• Sum of roots, $\alpha + \beta = -\frac{b}{a}$

• Product of roots, $\alpha \cdot \beta = \frac{c}{a}$

4. Quadratic Equation in Vertex Form:

• $y = a(x - h)^2 + k$, where (h,k) is the vertex of the parabola.

• If a > 0, the parabola opens upwards, and the vertex is the minimum point.

• If a < 0, the parabola opens downwards, and the vertex is the maximum point.

## Next Steps: Further Resources for Important Questions of JEE Advanced 2024 Quadratic Equations

Explore additional resources beyond JEE Advanced 2024 Quadratic Equations Important Questions. Students need to consider extra materials like practice papers, mock tests, PYQPs, etc., alongside important Quadratic Equations questions to gain a well-rounded preparation, refine their exam strategies, and build confidence for the JEE Advanced exam.

Make your JEE Advanced Maths studying for 2024 even better using our Important Questions organised by chapter. Find the links in the table below for easy access.

 JEE Advanced 2024: Chapter-Wise Links to Maths Important Questions PDF S.No Chapter Name 1 Sets, Relations and Functions 2 Algebra 3 Matrices 4 5 Trigonometry 6 Analytical Geometry 7 Differential Calculus 8 Integral Calculus 9 Vectors

1. According to chapter Quadratic Equations for JEE Advanced, what are the maximum and minimum values of roots of a quadratic equation?

For the equation ax2+bx+c,

If a <0, then the expression has the greatest value at x = -b/2a. The maximum value of the root is -D/4a.

If a >0, then the expression has the least value at x = -b/2a. The minimum value of the root is -D/4a.

2. Which book is best for preparing quadratic equations for JEE Advanced?

Many experts and toppers have suggested Govorov - function and quadratic equations practice quadratic equations for JEE advanced Maths. Students can buy the book online and offline. There is also material provided on Vedantu. Apart from textbooks, students are required to refer to previous year question papers and solve as many as possible to improve their scores in the exam.

3. Is it difficult to score well in JEE advanced Maths?

Students found it difficult to solve the maths part in JEE advanced 2020. However, with proper practice, some students have scored well in their exam and cleared it. Proper guidance is needed to have conceptual clarity. You can study various materials available on Vedantu for better understanding. To get some extra concepts, students can refer to previous year questions and also some reference books. Practicing as many questions as possible will reduce the time taken to solve problems in exams.

4. What are the 4 ways to solve a quadratic equation?

The four different methods to solve a Quadratic equation is factorization, using square roots, completing the square and finally using the quadratic formula. If the students are asked to solve an equation in a particular format, then they are supposed to do it respectively. If the question does not mention any particular format, the student may follow his choice to solve the equation.

5. How to access material related to JEE advanced from Vedantu?

Students have a lot of qualified material on Vedantu. They can visit the homepage of the website. Then click the study material tab on top. Then select the competitive exams tab and select JEE advanced from it. We provide all the material for free. Students can download it and study it offline or access it from their laptops, tablets and mobile phones. Vedantu also provides material for other competitive and board examinations.

6. How do you improve quadratic equations?

Quadratic equations are already in a good form (ax^2 + bx + c = 0) for solving for the unknown variable (x). However, you might want to:

• Factor the equation to reveal relationships between the roots (if possible).

• Complete the square to rewrite the equation in a form suitable for applying the quadratic formula.

7. Can a quadratic formula have two solutions?

Yes, a quadratic formula always has two solutions. These solutions may be:

• Two distinct real numbers (if the discriminant is positive).

• A repeated real number (if the discriminant is zero).

• Two complex numbers (if the discriminant is negative).

8. How many solutions can a quadratic equation have *?

A quadratic equation can have 0, 1, or 2 solutions. This depends on the discriminant $(b^2 - 4ac)$:

• Positive discriminant: 2 distinct real number solutions.

• Zero discriminant: 1 repeated real number solution.

• Negative discriminant: 2 complex number solutions (not real numbers).

9. How many solutions can a quadratic system have?

A quadratic system (two quadratic equations) can have 0, 1, 2, or 4 solutions, depending on the relationship between the equations.

10. Can a quadratic have 1 solution?

Yes, a quadratic equation can have 1 solution (repeated). This occurs when the discriminant is zero $(b^2 - 4ac = 0)$. In this case, the quadratic formula reduces to a single solution with a double root.

11. How many possible roots can a quadratic equation have?

A quadratic equation can have a maximum of 2 roots. These roots may be real numbers (as discussed above) or complex numbers.

12. Why is it called a quadratic equation?

The term "quadratic" refers to the degree of the highest term $(x^2)$ in the equation. A quadratic equation is a polynomial equation of the second degree.

13. How many variables does a quadratic equation have?

A quadratic equation typically has one variable, usually represented by x. However, you can have quadratic equations in multiple variables, but the equation itself would no longer be of the second degree.

14. What is the infinite solution of a quadratic equation?

Quadratic equations generally don't have infinite solutions. Their solutions are determined by the coefficients (a, b, and c) and can be 0, 1, or 2 as discussed earlier.