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[tex]f(x) = - 5 {x}^{2} + 10x + 8[/tex]
[tex]0 = - 5 {x}^{2} + 10x + 8[/tex]
[tex] - 5 {x}^{2} + 10x + 8 = 0[/tex]
[tex]delta = {10}^{2} - 4( - 5)(8)[/tex]
[tex]delta = 100 + 160[/tex]
[tex]delta = 260[/tex]
[tex]x = \frac{ - (10) + \sqrt{delta} }{2 \times ( - 5)} \\ [/tex]
[tex]x = \frac{ - 10 + \sqrt{260} }{ - 10} \\ [/tex]
[tex]x = \frac{ - 10 + 2 \sqrt{65} }{ - 10} \\ [/tex]
[tex]x = \frac{ - 5 + \sqrt{65} }{ - 5} \\ [/tex]
And
[tex]x = \frac{ - 10 - \sqrt{delta} }{ - 10} \\ [/tex]
[tex]x = \frac{ - 10 - 2 \sqrt{65} }{ - 10} \\ [/tex]
[tex]x = \frac{ 5 + \sqrt{65} }{5} \\ [/tex]
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Thus list the zeroes of the function is :
[tex]x = \frac{ - 5 + \sqrt{65} }{ - 5} \\ [/tex]
And
[tex]x = \frac{5 + \sqrt{65} }{5} \\ [/tex]
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