Find the roots of the quadratic equations by using the quadratic formula in each of the following:
$ 5 x^{2}+13 x+8=0 $

Given:

Given quadratic equation is \( 5 x^{2}+13 x+8=0 \).

To do:

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

Solution:

$5x^2+13x + 8 = 0$

The above equation is of the form $ax^2 + bx + c = 0$, where $a = 5, b = 13$ and $c =  8$

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

$=(13)^{2}-4 \times 5\times8$

$=169-160$

$=9$

$\mathrm{D}>0$

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

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

$=\frac{-13+\sqrt{9}}{2(5)}$

$=\frac{-13+3}{10}$

$=\frac{-10}{10}$

$=-1$

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

$=\frac{-13-\sqrt{9}}{2(5)}$

$=\frac{-13-3}{10}$

$=\frac{-16}{10}$

$=-\frac{8}{5}$

Hence, the roots of the given quadratic equation are $-\frac{8}{5}, -1$. 

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Updated on: 10-Oct-2022

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