Question
Solve the following quadratic equations by factorization:
$48x^2 - 13x - 1 = 0$
$48x^2 - 13x - 1 = 0$
✓
Answer
$48x^2 - 13x - 1 = 0$
$\Rightarrow 48x^2 - 16x + 3x - 1 = 0$
$\begin{cases}\because48\times(-1)=48\\\therefore-48=-16\times3\\-13=-16+3\end{cases}$
$\Rightarrow 16x(3x - 1) + 1(3x - 1) = 0$
$\Rightarrow (3x - 1)(16x + 1) = 0$
Either $3x - 1 = 0,$
Then $3x = 1$
$\Rightarrow\text{x}=\frac{1}{3}$
Or $16x + 1 = 0,$
Then $16x = -1$
$\Rightarrow\text{x}=\frac{-1}{16}$
Roots are $\text{x}=\frac{1}{3},\frac{-1}{16}$
$\Rightarrow 48x^2 - 16x + 3x - 1 = 0$
$\begin{cases}\because48\times(-1)=48\\\therefore-48=-16\times3\\-13=-16+3\end{cases}$
$\Rightarrow 16x(3x - 1) + 1(3x - 1) = 0$
$\Rightarrow (3x - 1)(16x + 1) = 0$
Either $3x - 1 = 0,$
Then $3x = 1$
$\Rightarrow\text{x}=\frac{1}{3}$
Or $16x + 1 = 0,$
Then $16x = -1$
$\Rightarrow\text{x}=\frac{-1}{16}$
Roots are $\text{x}=\frac{1}{3},\frac{-1}{16}$
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