# If the Difference Between the Roots of the Equation X 2 + a X + 8 = 0 is 2, Write the Values of A. - Mathematics

If the difference between the roots of the equation $x^2 + ax + 8 = 0$ is 2, write the values of a.

#### Solution

Given:

$x^2 + ax + 8 = 0 .$

Let $\alpha \text { and } \beta$ are the roots of the equation.
Sum of the roots = $\alpha + \beta = \frac{- a}{1} = - a$.

Product of the roots = $\alpha\beta = \frac{8}{1} = 8$

Given:

$\alpha - \beta = 2$

$\text { Then }, \left( \alpha + \beta \right)^2 - \left( \alpha - \beta \right)^2 = 4\alpha\beta$

$\Rightarrow \left( \alpha + \beta \right)^2 - 2^2 = 4 \times 8$

$\Rightarrow \left( \alpha + \beta \right)^2 - 4 = 32$

$\Rightarrow \left( \alpha + \beta \right)^2 = 32 + 4 = 36$

$\Rightarrow \left( \alpha + \beta \right) = \pm 6$

$\alpha + \beta = - a = \pm 6$

$a = \pm 6$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook