JEE Advanced Important Questions of Quadratic Equations
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Quadratic Equations Important Questions JEE Advanced
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
Roots of quadratic equation
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.
FAQs on JEE Advanced Quadratic Equations Important Questions
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 thewebsite. 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.