Question
Solve the following quadratic equations by factorization:
$9x^2 - 3x - 2 = 0$
$9x^2 - 3x - 2 = 0$
✓
Answer
We have
$9x^2 - 3x - 2 = 0$
$\Rightarrow 9x^2 - 6x + 3x -2 = 0$
$\Rightarrow 3x(3x - 2) + 1(3x - 2) = 0$
$\Rightarrow (3x - 2)(3x + 1) = 0$
$\Rightarrow $ either $3x - 2 = 0$ or $3x + 1 = 0$
$\Rightarrow 3x = 2 $or $3x = -1$
$\Rightarrow\text{x}=\frac{2}{3}$ or $\text{x}=-\frac{1}{3}$
Thus, $\text{x}=\frac{2}{3}$ and $\text{x}=-\frac{1}{3}$ are two roots of the equation $9x^2 - 3x - 2 = 0$
$9x^2 - 3x - 2 = 0$
$\Rightarrow 9x^2 - 6x + 3x -2 = 0$
$\Rightarrow 3x(3x - 2) + 1(3x - 2) = 0$
$\Rightarrow (3x - 2)(3x + 1) = 0$
$\Rightarrow $ either $3x - 2 = 0$ or $3x + 1 = 0$
$\Rightarrow 3x = 2 $or $3x = -1$
$\Rightarrow\text{x}=\frac{2}{3}$ or $\text{x}=-\frac{1}{3}$
Thus, $\text{x}=\frac{2}{3}$ and $\text{x}=-\frac{1}{3}$ are two roots of the equation $9x^2 - 3x - 2 = 0$
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