Question

if alpha and beta are the zeroes of polynomial x2-6x+a then find the value of if 3alpha+2beta =20

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

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@Answer..

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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.