Exercise 2.2: Relationship Between Zeroes and Coefficients
This is the most important exercise in Chapter 2. You'll find zeroes of quadratic polynomials and verify the relationship: sum of zeroes = -b/a, product of zeroes = c/a.
Extra Practice Questions
These questions cover the same concepts as Exercise 2.2. Try solving them to build confidence before or after the textbook exercise.
If α and β are the zeros of the polynomial f(x) = x² - (k+6)x + 2(2k-1), and α + β = αβ/2, then find the value of k.
If α and β are the zeros of the quadratic polynomial `f(x) = x² - 5x + 4`, find the value of `α² + β²`.
The graph of a polynomial `y = P(x)` intersects the x-axis at exactly three distinct points. What can be concluded about the number of zeros of `P(x)`?
If α and β are the zeros of the polynomial x² - px + q, then a polynomial whose zeros are 1/α and 1/β is:
If α and β are the zeros of the quadratic polynomial f(x) = x² - 5x + 4, then the value of α² + β² is:
Ravi was finding the sum of zeros for the quadratic polynomial x² - 7x + 10. He stated that the sum of zeros is 7. Is his calculation correct? If not, what is the correct sum?
If α and β are the zeros of the polynomial f(x) = x² + px + q, then find the value of (α/β + β/α).
If the sum of the zeros of the polynomial 2x² - (3k-1)x + 5 is equal to their product, find the value of k.
For any two polynomials p(x) and g(x), where g(x) ≠ 0, we can find polynomials q(x) and r(x) such that p(x) = g(x)q(x) + r(x). What is the essential condition for the remainder r(x) in this division algorithm?
If two zeros of the polynomial p(x) = x³ - 5x² - 2x + 24 are 3 and -2, then find its third zero.
Stuck on a question?
Paste any question from Exercise 2.2 into our AI Maths Solver and get a step-by-step solution instantly. It works for all NCERT questions.
Try AI Solver — FreeCommon Mistakes to Avoid
- ✗Sign errors when computing sum of zeroes (-b/a, not b/a)
- ✗Forgetting to verify the relationship after finding zeroes
- ✗Not being able to factorise the quadratic — practise splitting the middle term
- ✗Mixing up the formulas for sum and product
Other Exercises in Chapter 2
Frequently Asked Questions
How many questions are in NCERT Exercise 2.2?
Exercise 2.2 has 6 questions on finding zeroes of quadratic polynomials and verifying the sum-product relationship with coefficients.
What is the relationship between zeroes and coefficients?
For a quadratic ax² + bx + c with zeroes α and β: sum (α + β) = -b/a, product (αβ) = c/a. This is tested heavily in boards.
Is Exercise 2.2 important for board exams?
Very important. Questions from this exercise appear in almost every CBSE board paper — usually 2-3 marks.
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