Question

Find the zeroes of the polynomial and verify the relationship between the zeroes and the coefficients
4x^-17x-21

Answer 1

We have,

4x² - 17x - 21

By Splitting middle term

= 4x² - 21x + 4x - 21

= x ( 4x - 21 ) + 1 ( 4x - 21 )

= ( x + 1 ) ( 4x - 21 )

So,to find zeroes of the polynomial: 4x² - 17x - 21 will be 0.

Hence ( x + 1 ) = 0 and ( 4x - 21 ) = 0

So,

x = -1 and x = 21/4

Therefore, the zeroes of polynomial: 4x² - 17x - 21 are -1 and 21/4.

Verification:-

★ Sum of the zeroes: - Coefficient of x/Coefficient of x²

⇒ - 1 + 21/4 = - ( -17 ) / 4

⇒ -4 + 21 / 4 = 17 / 4

⇒ 17 / 4 = 17 / 4

★ Product of the zeroes: Constant term/Coefficient of x²

⇒ - 1 × 21/4 = -21/4

⇒ -21 / 4 = -21/4

verified.