Question

if alpha and beta are zeros of polynomial x square - 6 X + A and 3 alpha plus 2 Beta is equal to 2 then find a​

Answer 1

Step-by-step explanation:

Explanation

We are given the zeroes of a Quadratic equation x^2-6x+A as alpha and beta

And we are also given that 3alpha+2beta=2

Theory

So we know that Alpha+Beta is equal to -b/a

and we know that Alpha*Beta is equal to c/a

Procedure

Alpha+beta= -b/a = 6. -(1)

3alpha+2beta=2. -(2)

2(alpha+beta) =12

2alpha+2beta+ alpha= 2

12+ alpha=2

alpha= -10

For Remaining steps ,plz refer attachment

Value of A comes out to be -160

Answer 2

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.