Question

alpha and beta are zeroes of the polynomial x2 - 6x + 9 then find tje value of 2 beta

Answer 1

Polynomial P(x) = x² - 6 x + a

Given α and β are the roots. To find a , if 3 α + 2 β = 20. ---(1)

From the quadratic expression:

α + β = 6 ---(2)

and α β = a --- (3)

Multiply equation (2) by 2 and subtract from (1) to get:

α = 20 -12 = 8

Substitute this value in(2) to get:

β = 6-8 = -2

Substitute these in (3) to get: a = α β = -16

Answer 2

The zeroes of the polynomial of x^2 - 6x + 9 are alpha and beta

Factorising the equation x^2 - 6x + 9 = 0 , we get

x^2-3x-3x+9=0

x(x-3)-3(x-3) = 0

(x-3)(x-3) = 0

x = 3

Therefore,

Alpha = beta = x = 3

Therefore,

2 beta = 2*3 = 6