Solve the following quadratic equations by factorization method:
$2 (x + 1)^{2} - 5 (x + 1) = 12$

{- \frac{5}{2}, 3}

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{\frac{5}{2}, 3}

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{- \frac{5}{2}, - 3}

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None of these

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Solution

The correct option is A ${- \frac{5}{2}, 3}$
$2 (x + 1)^{2} - 5 (x + 1) = 12$
$\Rightarrow$ $2 (x^{2} + 2 x + 1) - 5 x - 5 = 12$
$\Rightarrow$ $2 x^{2} + 4 x + 2 - 5 x - 5 = 12$
$\Rightarrow$ $2 x^{2} - x - 15 = 0$
$\Rightarrow$ $2 x^{2} - 6 x + 5 x - 15 = 0$
$\Rightarrow$ $2 x (x - 3) + 5 (x - 3) = 0$
$\Rightarrow$ $(x - 3) (2 x + 5) = 0$
$\Rightarrow$ $x - 3 = 0$ and $2 x + 5 = 0$
$∴$ $x = 3$ and $x = - \frac{5}{2}$

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Similar questions

3 x^{2} - 5 x - 12 = 0

\sqrt{5} x^{2} + 2 x - 3 \sqrt{5} = 0

Solve the following quadratic equation by factorization.
$\frac{x + 3}{x + 2} = \frac{3 x - 7}{2 x - 3}, x \neq - 2, \frac{3}{2}$

\sqrt{5} x^{2} + 2 x = 3 \sqrt{5}

\frac{4}{x} - 3 = \frac{5}{2 x + 3} x \neq 0, \frac{- 3}{2}

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