Question

22
1. Find the zeroes of the following quadratic polynomials and verify the relationship between
the zeroes and the coefficients.
(1) x2 - 2x - 8
​

Answer 1

Given:

☛ p(x) = x² - 2x - 8

To Find:

☛ zeroes of the polynomial p(x)

Also,

Verify the relationship between the zeroes and the coefficients.

Solution:

☛ p(x) = x² - 2x - 8

➜ x² - 4x + 2x - 8

➜ x ( x - 4) + 2 ( x - 4)

➜ (x - 4)(x + 2)

Zeroes are 4 and -2

Also,

☛ sum of zeroes = - coefficient of x / coefficient of x²

➜ 4 + (-2) = -(-2)/1

➜ 4 - 2 = 2

➜ 2 = 2

☛ Product of zeroes = constant term / coefficient of x²

➜ 4 × -2 = -8/1

➜ -8 = -8

Hence, Proved.