Question
Solve the following quadratic equations by factorization:
$3x^2 - 14x - 5 = 0$
$3x^2 - 14x - 5 = 0$
✓
Answer
$3x^2 - 14x - 5 = 0$
$\Rightarrow 3x^2 - 15x + x - 5 = 0$
$\begin{cases}\because -5\times3=-15& \\\therefore-15=-15\times1\\-14=-15+1\end{cases}$
$\Rightarrow 3x(x - 5) + 1(x - 5) = 0$
$\Rightarrow (x - 5)(3x + 1) = 0$
Either $x - 5 = 0$, then $x = 5$ or $3x + 1 = 0,$
Then $3x = -1$
$\Rightarrow\text{x}=\frac{-1}{3}$
Roots are x = 5, $\frac{-1}{3}$
$\Rightarrow 3x^2 - 15x + x - 5 = 0$
$\begin{cases}\because -5\times3=-15& \\\therefore-15=-15\times1\\-14=-15+1\end{cases}$
$\Rightarrow 3x(x - 5) + 1(x - 5) = 0$
$\Rightarrow (x - 5)(3x + 1) = 0$
Either $x - 5 = 0$, then $x = 5$ or $3x + 1 = 0,$
Then $3x = -1$
$\Rightarrow\text{x}=\frac{-1}{3}$
Roots are x = 5, $\frac{-1}{3}$
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