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If the sum of the roots of the equation $a x^2+b x+c=0$ be equal to the sum of their squares, then
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1761 Upvotes
Verified Answer
The correct answer is:
$b(a+b)=2 a c$
$\alpha+\beta=\alpha^2+\beta^2$
$\frac{-b}{a}=(\alpha+\beta)^2-2 \alpha \beta$
$-\frac{b}{a}=\frac{b^2}{a^2}-\frac{2 c}{a}$
$\therefore \frac{b}{a}+\frac{2 c}{a}=\frac{b^2}{a^2}$
$\frac{-b+2 c}{a}=\frac{b^2}{a^2}$
$-a b+2 a c=b^2$
$2 a c=b^2+a b$
$2 a c=b(a+b)$
Option 3 is correct
$\frac{-b}{a}=(\alpha+\beta)^2-2 \alpha \beta$
$-\frac{b}{a}=\frac{b^2}{a^2}-\frac{2 c}{a}$
$\therefore \frac{b}{a}+\frac{2 c}{a}=\frac{b^2}{a^2}$
$\frac{-b+2 c}{a}=\frac{b^2}{a^2}$
$-a b+2 a c=b^2$
$2 a c=b^2+a b$
$2 a c=b(a+b)$
Option 3 is correct
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