Class 10 / Maths

Class 10 Maths Polynomials Worksheet

Practice zeros of quadratic polynomials and relationships between zeros and coefficients.

advanced40 minutesAnswer key included

Learning objective

Practise finding zeros, using relationships between zeros and coefficients, forming quadratic polynomials, and interpreting real zeros graphically.

Questions

  1. Find the zeros of x^2 - 3x - 10.
  2. Find the sum and product of zeros of 3x^2 - 8x + 4.
  3. Verify the relationship between zeros and coefficients for x^2 + 5x + 6.
  4. Form a quadratic polynomial whose zeros are 4 and 7.
  5. Form a quadratic polynomial whose zeros are -3 and 2.
  6. If one zero of 2x^2 + kx + 3 is 3, find k.
  7. Find k if the sum of zeros of x^2 + kx + 12 is 7.
  8. Find the value of p if the product of zeros of 5x^2 - 8x + p is 6.
  9. Check whether 2 and 3 are zeros of x^2 - 5x + 6.
  10. How many real zeros can a quadratic polynomial have? Explain with graph positions.

Answer key

Show suggested answers
  1. x^2 - 3x - 10 = (x - 5)(x + 2), so zeros are 5 and -2.
  2. For 3x^2 - 8x + 4, sum = -b/a = 8/3 and product = c/a = 4/3.
  3. x^2 + 5x + 6 = (x + 2)(x + 3), zeros are -2 and -3. Sum = -5 = -b/a and product = 6 = c/a.
  4. Polynomial = (x - 4)(x - 7) = x^2 - 11x + 28.
  5. Polynomial = (x + 3)(x - 2) = x^2 + x - 6.
  6. If x = 3 is a zero, 2(9) + 3k + 3 = 0, so 21 + 3k = 0 and k = -7.
  7. For x^2 + kx + 12, sum of zeros = -k. Given sum = 7, so k = -7.
  8. Product of zeros = p/5. If product is 6, p = 30.
  9. For x = 2, p(x) = 0. For x = 3, p(x) = 0. So both are zeros.
  10. A quadratic polynomial can have two real zeros, one repeated real zero, or no real zero depending on whether its graph cuts, touches, or does not meet the x-axis.

How to use this worksheet

Students can solve the questions independently first, then review errors with a parent or teacher. Teachers can use it as a short class activity, homework sheet, or revision check.

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