Solve the following quadratic equations by factorization: 3x^2 = … - Vidyadip

Question

Solve the following quadratic equations by factorization:
$3x^2 = -11x - 10$

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Answer

$3x^2 = -11x - 10$
$\Rightarrow 3x^2 + 11x + 10 = 0$
$\Rightarrow 3x^2 + 11x + 10 = 0$
$\begin{cases}\because3\times10=30\\\therefore30=5\times6\\11=5+6\end{cases}$
$\Rightarrow 3x^2 + 6x + 5x + 10 = 0$
$\Rightarrow 3x(x + 2) + 5(x + 2) = 0$
$\Rightarrow (x + 2)(3x + 5) = 0$
Either $x + 2 = 0$, then $x = -2$
Or $3x + 5 = 0$. then $3x = -5$
$\Rightarrow\text{x}=\frac{-5}{3}$
$\therefore$ Roots are $x = -2$, $\frac{-5}{3}$

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