Question

find the value of 'a'for which the root αand β of the equation x^2-6x+a=0. satisfy the realtion 3α+2β=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.

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Answer 2

α + β = 6

β = 6- a

3α + 2β = 28

3α + 2(6-a) = 20

α = 20 - 12

α = 8

substituting x= 8 in the equation

64 - 48 + a = 0

a = - 16

hope it helped you