# 17 X 2 + 28 X + 12 = 0 - Mathematics

$17 x^2 + 28x + 12 = 0$

#### Solution

Given:

$17 x^2 + 28x + 12 = 0$

Comparing the given equation with the general form of the quadratic equation

$a x^2 + bx + c = 0$, we get
$a = 17, b = 28$ and $c = 12$
Substituting these values in $\alpha = \frac{- b + \sqrt{b^2 - 4ac}}{2a}$ and $\beta = \frac{- b - \sqrt{b^2 - 4ac}}{2a}$ , we get:
$\alpha = \frac{- 28 + \sqrt{784 - 4 \times 17 \times 12}}{34}$  and   $\beta = \frac{- 28 - \sqrt{784 - 4 \times 17 \times 12}}{34}$
$\Rightarrow \alpha = \frac{- 28 + \sqrt{784 - 816}}{34}$ and  $\beta = \frac{- 28 - \sqrt{784 - 816}}{34}$
$\Rightarrow \alpha = \frac{- 28 + \sqrt{- 32}}{34}$ and $\beta = \frac{- 28 - \sqrt{- 32}}{34}$
$\Rightarrow \alpha = \frac{- 28 + \sqrt{32 i^2}}{34}$    and $\beta = \frac{- 28 - \sqrt{32 i^2}}{34}$
$\Rightarrow \alpha = \frac{- 28 + 4\sqrt{2} i}{34}$  and $\beta = \frac{- 28 - 4\sqrt{2} i}{34}$
$\Rightarrow \alpha = \frac{- 14 + 2\sqrt{2} i}{17}$   and   $\beta = \frac{- 14 - 2\sqrt{2} i}{17}$
Hence, the roots of the equation are $- \frac{14}{17} \pm \frac{2\sqrt{2}}{17}i .$
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook