Question
Solve quadratic equation using formula : x ² + 10 x + 2 = 0
✓
Answer
$x^2+10 x+2=0$ comparing with $a x^2+b x+c=0$
we get $a=1, b=10, c=2$,
$\begin{aligned}
\therefore b^2-4 a c & =(10)^2-4 \times 1 \times 2 \\
& =100-8 \\
& =92
\end{aligned}$
$\begin{aligned}
x & =\frac{-b \pm \sqrt{b^2-4 a c}}{2 a} \\
& =\frac{-10 \pm \sqrt{92}}{2 \times 1} \\
x & =\frac{-10 \pm \sqrt{4 \times 23}}{2}
\end{aligned}$
$\begin{aligned}
& =\frac{-10 \pm 2 \sqrt{23}}{2} \\
& =\frac{2(-5 \pm \sqrt{23})}{2} \\
\therefore x & =-5 \pm \sqrt{23} \\
\therefore x & =-5+\sqrt{23} \text { or } x=-5-\sqrt{23}
\end{aligned}$
$\therefore$ the roots of the given quadratic equation are $-5+\sqrt{23}$ and $-5-\sqrt{23}$.
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