Question

Verify the relationship between the zeroes and coefficients of the following polynomail x^2+11×+18

Answer 1

We have,

x² + 11x + 18

★ By Splitting middle term

⇒ x² + 9x + 2x + 18

⇒ x ( x + 9 ) + 2 ( x + 9 )

⇒ ( x + 9 ) ( x + 2 )

So, to find zeroes of polynomial : x² + 11x + 18 will be 0,

Hence ( x + 9 ) = 0 and ( x + 2 ) = 0

⇒ x = -9 and x = -2

Therefore, the zeroes of the polynomial are -9 and -2 .

Verification:-

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

⇒ ( -9 ) + ( -2 ) = - 11 / 1

⇒ - 11 = -11

L.H.S = R.H.S

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

⇒ ( -9 ) × ( -2 ) = 18 / 1

⇒ 18 = 18

L.H.S = R.H.S

Verified.