Question

Select the approximate values of x that are solutions to f(x) = 0, where f(x) = -8x^2 + 8x + 5.

Answer 1

$f(x)=-8x^2+8x+5\\\\f(x)=0\iff-8x^2+8x+5=0\\\\a=-8;\ b=8;\ c=5\\\\\Delta=b^2-4ac\\\\\Delta=8^2-4\cdot(-8)\cdot5=64+160=224\\\\x_1=\frac{-b-\sqrt\Delta}{2a};\ x_2=\frac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{224}\approx\sqrt{225}=15\\\\x_1\approx\frac{-8-15}{2\cdot(-8)}=\frac{-23}{-16}=1\frac{7}{16}\approx1.5\\\\x_2\approx\frac{-8+15}{2\cdot(-8)}=\frac{7}{-16}=-\frac{7}{16}\approx-0.5$