# 4x2 − 12x + 25 = 0 - Mathematics

4x2 − 12x + 25 = 0

#### Solution

We have:

$4 x^2 - 12x + 25 = 0$

$\Rightarrow 4 x^2 - 12 x + 9 + 16 = 0$

$\Rightarrow (2x )^2 + 3^2 - 2 \times 2x \times 3 - (4i )^2 = 0$

$\Rightarrow (2x - 3 )^2 - (4i )^2 = 0$

$\Rightarrow (2x - 3 + 4i) (2x - 3 - 4i) = 0 [ a^2 - b^2 = (a + b) (a - b)]$

$\Rightarrow (2x - 3 + 4i) = 0$ or, $(2x - 3 - 4i) = 0$

$\Rightarrow 2x = 3 - 4i$  or, $2x = 3 + 4i$

$\Rightarrow x = \frac{3}{2} - 2i$  or, $x = \frac{3}{2} + 2i$

Hence, the roots of the equation are $\frac{3}{2} - 2i \text { and } \frac{3}{2} + 2i$ .

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook