Question

if α and β are the zeroes of the polynomial x²+x-6.
Then find (1/α)² + (1/β)²​

Answer 1

Given

α and β are the zeroes of the polynomial x²+x-6

To Find

(1/α)²+(1/β)²

Solution

Find the zeroes of the polynomial

⇒x²+x-6 = 0

⇒x²+(3-2)x-6 = 0

⇒x²+3x-2x-6 = 0

⇒x(x+4)-2(x+3) = 0

⇒(x+3) (x-2) = 0

• zeroes

x+3 = 0 ; x = (-3)

x-2 = 0 x = 2

• α = (-3)
• β = 3

Now finding the value of 1/α + 1/β

⇒(1/α)15 = 1/-3 = (-1/3)²

⇒1/α² = 1/9

⇒(1/β) = (1/2)²

⇒(1/α)²+(1/β)²

⇒1/9 + 1/4

⇒13/36

★ Hence, (1/α)²+(1/β)² = 13/36