Question

If $\alpha ,\beta$ are the roots of the equation $a{x}^2+bx+c=0$, then find ${\alpha }^2+{\beta }^2$.

• A. $\frac{b^2+4ac}{4a}$
• B. $\frac{4ac-b^2}{2a}$
• C. $\frac{b^2-2ac}{a^2}$
• D. $\frac{b^2-4ac}{a^2}$

Answer 1

Answer: (C)

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

${\alpha }^2+\beta 2=(\alpha +\beta {)}^2-2\alpha \beta$

$\alpha +\beta =-b/a$ and $\alpha \beta =c/a$

$\Rightarrow {\alpha }^2+{\beta }^2=b^2/a^2-2\times c/a$

$\therefore {\alpha }^2+{\beta }^2=\frac{b^2-2ac}{a^2}$