Express q as a function of p, given that one root of x^2 + px + q = 0 is twice the other.
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Express q as a function of p, given that one root of x^2 + px + q = 0 is twice the other.
x2 = 2*x1
(x-x1)(x-2*x1) = x^2+p*x+q
x^2-(2*x1+x1)*x+2*(x1^2) = x^2+p*x+q
x^2-(3*x1)*x+2*(x1^2) = x^2+p*x+q
So:
p = -3*x1
q = 2*(x1^2)
or:
x1 = (-1/3)p
so:
q = (2/9)*(p^2)