Question

The coefficient of $x$ in the quadratic equation $x^2+px+q=0$ was taken as $-14$ in place of $-10$, its roots were found to be $6,4$. If $\alpha ,\beta$ are the roots of correct equation, then the value of ${\alpha }^2+{\beta }^2$ must be equal to

__

• A. 52.0
• B. 52
• C. 52.00

Answer 1

Answer: (A), (B), (C)

$q=24[$product of roots $=6\times 4]$

$p=-10$ [negative of Sum of the roots]

$\therefore$ The equation is $x^2-10x+24=0$

The roots are $6,4$

$\therefore {\alpha }^2+{\beta }^2=6^2+4^2$

$=36+16$

$=52$