C1: Stuck!

[TheFly]

Had to do this for hwk.
Got ne ideers

p(x)=x-6x-3 and q(x)=x-2x+4. The polynomial p(x)+aq(x), where a is a constant, is a perfect square.

Calculate the 2 possible values of a.

[KatieB]

p(x)=x-6x-3 and q(x)=x-2x+4. The polynomial p(x)+aq(x), where a is a constant, is a perfect square.

p(x)+aq(x) ≡x-6x-3 + a(x-2x+4)
≡(1+a)x -(6+2a)x +(4a-3)
for a percect square the roots must be equal so b-4ac=0


(6+2a)-4(1+a)(4a-3) = 0
36+24a+4a-4(4a-3+4a-3a) = 0
36+24a+4a-16a+12-16a+12a = 0
12a-20a-48 = 0
divide by 4
3a-5a-12=0
(3a + 4)(a - 3) = 0
so a=-4/3 and a=3