Question

Find the quadratic polynomial whose zeroes are -2 and -5. Verify the relationship between zeroes and coefficients of the polynomial.

Answer 1

Answer:

The zeroes are -2 and -5

Sum of the zeroes = -2 + -5 = -7

i. e., alpha + beta = -7

Product of zeroes = -2 × -5 = 10

i. e., alpha × beta = 10

Then the polynomial is of the form

x² - (alpha + beta) × x + (alpha × beta) = 0

x² - (-7) × x + 10 = 0

x² + 7x + 10 = 0

Equation is x² + 7x + 10

-b/a = -7/1 = -7

i. e., -b/a = alpha + beta

c/a = 10/1 = 10

i. e., c/a = alpha × beta

Hence the relationship is verified.