# Find the roots of the quadratic equations by using the quadratic formula in each of the following:$x^{2}+2 \sqrt{2} x-6=0$

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Given:

Given quadratic equation is $x^{2}+2 \sqrt{2} x-6=0$.

To do:

We have to find the roots of the given quadratic equation.

Solution:

$x^{2}+2 \sqrt{2} x-6=0$

The above equation is of the form $ax^2 + bx + c = 0$, where $a = 1, b = 2 \sqrt{2}$ and $c =-6$

Discriminant $\mathrm{D} =b^{2}-4 a c$

$=(2 \sqrt{2})^{2}-4 \times (1)\times(-6)$

$=8+24$

$=32$

$\mathrm{D}>0$

Let the roots of the equation are $\alpha$ and $\beta$

$\alpha =\frac{-b+\sqrt{\mathrm{D}}}{2 a}$

$=\frac{-2 \sqrt{2}+\sqrt{32}}{2(1)}$

$=\frac{-2 \sqrt{2}+4\sqrt2}{2}$

$=\frac{2\sqrt2}{2}$

$=\sqrt2$

$\beta =\frac{-b-\sqrt{\mathrm{D}}}{2 a}$

$=\frac{-2 \sqrt{2}-\sqrt{32}}{2(1)}$

$=\frac{-2 \sqrt{2}-4\sqrt{2}}{2}$

$=\frac{-6\sqrt{2}}{2}$

$=-3\sqrt2$

Hence, the roots of the given quadratic equation are $\sqrt2, -3\sqrt2$.

Updated on 10-Oct-2022 13:27:26