Question

If α and β are the zeroes of the quadratic polynomial
f(x) = 9x^2 - 9x + 2, then find the quadratic polynomial whose zeroes are
(α + β)*2 and (α - β) ^2 .

Answer 1

Answer:

f(x) = 9x² - 9x + 2 (1)

Quadratic equation is in the form of,

f(x) = x²-(α+β)x +αβ = 0

Frm (1), α+β = 9/9 = 1

αβ = 2/9

(α+β)² = (1)² = 1

α²+β²+2αβ = 1

α²+β² = 1-2(2/9)

= 1 - 4/9

= (9-4) / 9

= 5/9

(α-β)² = α²+β² - 2αβ

= 5/9 - 4/9

= 1/9

The quadratic polynomial whose zeroes are (α + β)² and (α - β)²,

α+β = (α + β)² + (α - β)²

= 1 + 1/9

= 10/9

αβ = (α + β)² • (α - β)²

= 1/9

q(x) = x²-10x/9 +1/9 = 0

(×9) 9x²-10x+1 = 0