Question

Find a polynomial whose zeroes are square of the zeroes of the polynomial. 3x square +6x- 9​

Answer 1

Answer:

Sol: Given polynomial 3x2 + 6x - 9 = 0 ⇒ 3x2 + 9x -3x - 9 = 0 3x( x + 3) -3( x + 3) = 0 3x - 3 = 0 , x + 3 = 0 x = 1 , x = - 3. Given that zeroes are square of the zeroes of the polynomial so that x = 1, 9 Sum of the roots α + β = 10. Product of the roots αβ = 9 According to the question x2 -(α + β)x + αβ = 0 ∴ the polynomial is x2 -10x + 9 = 0.