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bazaltina [42]3 years ago

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Answer:gotta go sorry

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Determine the zeros of the function <br> 5) y=-x² + 2x + 1

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<h3>Zeros of function are $x = 1 + \sqrt{2} \text{ and } x = 1 - \sqrt{2}$ </h3>

<em><u>Solution:</u></em>

<em><u>We have to find the zeros of the function</u></em>

$y = -x^2 + 2x+1$

Find the zeros of function:

$-x^2 + 2x+1 = 0\\\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=-1,\:b=2,\:c=1\\\\x =\frac{-2\pm \sqrt{2^2-4\left(-1\right)1}}{2\left(-1\right)}$

$Simplify\\\\x=\frac{-2 \pm \sqrt{4+4}}{-2}\\\\x =\frac{-2 \pm \sqrt{8}}{-2}\\\\Simplify\\\\x =\frac{-2 \pm 2 \sqrt{2}}{-2}\\\\x = 1 \pm \sqrt{2}$

We have two zeros

$x = 1 + \sqrt{2} \text{ and } x = 1 - \sqrt{2}$

Thus zeros of function are $x = 1 + \sqrt{2} \text{ and } x = 1 - \sqrt{2}$

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