Question

If sum of the roots of the equation $a{x}^2+bx+c=0$ is equal to the sum of their squares, then

• A. $2ac=ab+c$
• B. $2ac=b(a+b)$
• C. $a^2+b^2=c^2$
• D. $a^2+b^2=a+b$

Answer 1

Answer: (B)

$2ac=b(a+b)$

Sum of the roots of the equation $a{x}^2+bx+c=0$ is equal to the sum of their squares.

Let $\alpha ,\beta$ be the roots.

$\Rightarrow \alpha +\beta =\frac{-b}{a}$ and $\alpha \beta =\frac{c}{a}$

$\alpha +\beta ={\alpha }^2+{\beta }^2$

$\frac{-b}{a}={\left(\frac{-b}{a}\right)}^2-2\left(\frac{c}{a}\right)$

$=\frac{b^2-2ac}{a^2}$

$\Rightarrow -ab=b^2-2ac$

$\therefore 2ac=b(a+b)$

Hence, option B.