Question

If $\alpha \&\beta$ are roots of quadratic equation $x^2+13x+8=0$ then the value of ${\alpha }^4+{\beta }^4=$

• A. $23281$
• B. $23218$
• C. $23128$
• D. $23182$

Answer 1

The correct option is A $23281$

$x^2+13x+8=0$

$\begin{array}{c}\alpha +\beta =-13\\ \alpha \beta =8\end{array}|{\alpha }^4+{\beta }^4$

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

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

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

$=\left[\right(\alpha +\beta {)}^2-2\alpha \beta {]}^2-2(\alpha \beta {)}^2$

$=[169-16{]}^2-2\times 64$

$=(153{)}^2-128$

$=23,409-128$

$=23281$