Question

if alpha and beta are roots of equation x2 -6x=k such that 3aplha +2beta=20 find k

Answer 1

x^2 - 6k + k

x^2 - 6x + k = 0

therefore, alpha + beta = -(-6)/1

alpha + beta = 6 -(1)

3alpha + 2beta = 20

- alpha + alpha + alpha + beta + beta = 20

- (alpha + beta) +( alpha + beta) + beta = 20

sub with eq(1), we get -

6+6+alpha = 20

so, alpha = 8

beta = 6 - alpha = 6-8 = -2

alpha(beta) = k/1

8(-2) = k

therefore k = -16