Question

Use the equation to help list the zeros of the function.

Answer 1

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$f(x) = - 5 {x}^{2} + 10x + 8$

$0 = - 5 {x}^{2} + 10x + 8$

$- 5 {x}^{2} + 10x + 8 = 0$

$delta = {10}^{2} - 4( - 5)(8)$

$delta = 100 + 160$

$delta = 260$

$x = \frac{ - (10) + \sqrt{delta} }{2 \times ( - 5)}$

$x = \frac{ - 10 + \sqrt{260} }{ - 10}$

$x = \frac{ - 10 + 2 \sqrt{65} }{ - 10}$

$x = \frac{ - 5 + \sqrt{65} }{ - 5}$

And

$x = \frac{ - 10 - \sqrt{delta} }{ - 10}$

$x = \frac{ - 10 - 2 \sqrt{65} }{ - 10}$

$x = \frac{ 5 + \sqrt{65} }{5}$

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Thus list the zeroes of the function is :

$x = \frac{ - 5 + \sqrt{65} }{ - 5}$

And

$x = \frac{5 + \sqrt{65} }{5}$

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