Question

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

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

Answer 1

The correct option is A

$23281$

Explanation for the correct option:

Find the value of ${ɑ}^4+{\beta }^4$:

Given, $ɑ,\beta$ are the roots of quadratic equation $x^2+13x+8=0$

$\Rightarrow$$ɑ+\beta =–13,ɑ\beta =8$

As we know,

$\begin{array}{rcl}{ɑ}^2+{\beta }^2& =& {(ɑ+\beta )}^2–2ɑ\beta \\ & =& 153\end{array}$

$\begin{array}{rcl}\therefore {ɑ}^4+{\beta }^4& =& ({ɑ}^2+{\beta }^2)–2{ɑ}^2{\beta }^2\\ & =& \mathbf{23281}\end{array}$

Hence, Option ‘A’ is Correct.