Question

Find roots of the quadratic equation x² - 5x - 2 =0 by using quadratic formula

Answer 1

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Answer 2

The given equation is

x² - 5x - 2 =0

we have to find the roots of the quadratic equation by using a quadratic formula.

here a=1,b=-5 and c= -2.

The quadratic formula is

$\frac{ ( - b) + - \sqrt{ {b}^{2} - 4ac} }{2a}$

First we have to find the nature of roots by

${b}^{2} - 4ac$

${( - 5)}^{2} - 4(1 \times - 2) \\ 25 - ( - 8) \\ 25 + 8 = 33 \\ 33 > 0$

Therefore it has 2 distinct roots.

sub values in the quadratic formula.

$\frac{( - 25) + - \sqrt33}{2(1)} \\ \frac{ - 25 + \sqrt{}33}{2} and \frac{ - 25 - \sqrt{} 33}{2}$

Therefore, the above expression is the final answer.

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