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Solving a Quadratic Equation by Factorization Method

Solve : 4x2...

Question

Solve : $4 x^{2} - 4 x - 3 = 0$

A

x = 3/2, -1/2

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B

x = -1/2, -3/2

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C

x = 3/2, 1/2

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D

x = 1/2, 1

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Solution

The correct option is A x = 3/2, -1/2
$4 x^{2} - 4 x - 3 = 0$

$\Rightarrow$ $4 x^{2} - 6 x + 2 x - 3 = 0$

$\Rightarrow$ $2 x (2 x - 3) + 1 (2 x - 3) = 0$
$\Rightarrow$ $(2 x - 3) (2 x + 1) = 0$

$\Rightarrow$ $2 x - 3 = 0$ and $2 x + 1 = 0$

$\Rightarrow$ $2 x = 3$ and $2 x = - 1$

$∴$ $x = \frac{3}{2}$ and $x = \frac{- 1}{2}$

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