RS Aggarwal Solutions Class 10 Chapter 10 - Quadratic Equations (Ex 10B) Exercise 10.2 - Free PDF
FAQs on RS Aggarwal Solutions Class 10 Chapter 10 - Quadratic Equations (Ex 10B) Exercise 10.2
1. How do I use the quadratic formula to find solutions for questions in RS Aggarwal Class 10 Maths Ex 10B?
To correctly solve any problem in Ex 10B using the quadratic formula, you should follow this step-by-step method:
1. First, write the given equation in the standard form: ax² + bx + c = 0.
2. Carefully identify the values of the coefficients a, b, and c, paying close attention to their signs.
3. Calculate the discriminant (D) using the formula D = b² - 4ac.
4. Substitute the values of a, b, and √D into the quadratic formula, which is x = [-b ± √D] / 2a.
5. Calculate the two possible values for x, which represent the roots of the equation.
2. What is the most important first step when solving a problem from RS Aggarwal Ex 10B that is not in standard form?
The most crucial first step is to rearrange the given equation into the standard form of a quadratic equation, which is ax² + bx + c = 0. Many problems in this exercise may present the equation with terms on both sides of the equals sign or with fractions. Before you can apply the quadratic formula, you must simplify and move all terms to one side to correctly identify the 'a', 'b', and 'c' coefficients.
3. How does the discriminant (b² - 4ac) help determine the nature of roots for a quadratic equation?
The discriminant is a key component of the quadratic formula that tells you about the type of solutions an equation will have, which is a required step in the CBSE pattern. For any quadratic equation in your syllabus:
- If D > 0 (the discriminant is positive), the equation will have two distinct real roots.
- If D = 0, the equation will have two equal real roots (effectively one solution).
- If D < 0 (the discriminant is negative), the equation has no real roots.
Calculating this first helps verify the kind of answer to expect.
4. What are some common mistakes to avoid when solving quadratic equations in Ex 10B using the quadratic formula?
When solving RS Aggarwal problems, students should be careful to avoid these common errors:
- Incorrect Signs: Misinterpreting the signs of coefficients 'a', 'b', and 'c', especially if a term is negative (e.g., in x² - 5x + 3 = 0, b = -5).
- Mistake in '-b': Forgetting that the '-b' in the formula means taking the opposite sign of the original 'b' value.
- Division Error: Dividing only the square root part by 2a instead of the entire numerator (-b ± √D).
- Calculation Errors: Making simple arithmetic mistakes when calculating the discriminant, particularly with negative numbers.
5. Why is it a good strategy to find the discriminant before solving the entire quadratic formula?
Calculating the discriminant (D = b² - 4ac) first is an efficient problem-solving technique for exams. It acts as a quick check to predict the outcome. If you calculate D and find that it is negative, you immediately know there are no real solutions as per the CBSE Class 10 syllabus. This allows you to state the answer directly without needing to complete the rest of the quadratic formula calculation, saving valuable time.
6. What is the correct way to write the answer if the discriminant is negative for a question in Ex 10B?
If your calculation for the discriminant (D) results in a negative value, it means the equation has no real roots. This is because you cannot find the square root of a negative number within the real number system studied in Class 10. As per the CBSE 2025-26 guidelines, the correct final answer to write is that the equation has "no real roots" or "the roots are not real."
