The zeros of the given equation are 3.61 and -1.11
From the question, we are to determine the zeros of the given equation
The given equation is
y=-2x²+5x+8
To determine the zeros, we will set the equation to equal zero
That is
-2x²+5x+8 = 0
This can be written as
2x²-5x-8 = 0
Using the quadratic formula
[tex]x = \frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]
a = 2, b= -5, and c = -8
Putting these into the formula, we get
[tex]x = \frac{-(-5)\pm\sqrt{(-5)^{2}-4(2)(-8) } }{2(2)}[/tex]
[tex]x = \frac{5\pm\sqrt{25+64 } }{4}[/tex]
[tex]x = \frac{5\pm\sqrt{89 } }{4}[/tex]
[tex]x = \frac{5\pm 9.43}{4}[/tex]
[tex]x = \frac{5+9.43}{4} \ OR \ x = \frac{5-9.43}{4}[/tex]
[tex]x = \frac{14.43}{4} \ OR \ x = \frac{-4.43}{4}[/tex]
x = 3.61 OR x = -1.11
Hence, the zeros of the given equation are 3.61 and -1.11
Learn more on Quadratic equation here: https://brainly.com/question/8649555
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