Quadratic fun-3

Algebra Level 3

Find the sum of all values of x x for which the roots g g and h h of the equation

t 2 − 8 t + x = 0 t^{2}-8t+x=0

satisfy the condition that

g 2 + h 2 = 4 g^{2}+h^{2}=4

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The answer is 30.

Anik Mandal by Anik Mandal , 21, India

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1 solution

Aaaaa Bbbbb
Oct 3, 2014

Applyi Viet theory: g h = c a = x gh=\frac{c}{a}=x g + h = 8 g+h=8 g 2 + b 2 = 64 − 2 x = 4 g^2+b^2=64-2x=4 ⇒ x = 30 \Rightarrow x=\boxed{30}

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