Question

Select the approximate values of x that are solutions to f(x) = 0, where
f(x) = -9x2 + 4x + 9.

Answer 1

`f(x) = -9x^2 + 4x + 9\ \ \ and\ \ \ f(x)=0\\\\-9x^2 + 4x + 9=0\ \ \ \Leftrightarrow\ \ \ 9x^2 - 4x + (4)/(9) -(4)/(9)- 9=0\\\\(3x-(2)/(3))^2=9(4)/(9)\ \ \ \Leftrightarrow\ \ \ (3x-(2)/(3))^2= (85)/(9) \\\\3x-(2)/(3)= ( √(85) )/(3) \ \ \ or\ \ \ \ \ \ 3x-(2)/(3)= -( √(85) )/(3)\\\\3x= (2+ √(85) )/(3) \ \ \ \ \ \ or\ \ \ \ \ \ 3x= (2- √(85) )/(3)\\\\ x= (2+ √(85) )/(9) \ \ \ \ \ \ \ \ or\ \ \ \ \ \ \ x= (2- √(85) )/(9)\\\\`


`x\approx1.247\ \ \ \ \ \ \ \ or\ \ \ \ \ \ \ x\approx-0.802`

Answer 2

`f(x)=-9x^2+4x+9\\\\a=-9;\ b=4;\ c=9\\\\\Delta=b^2-4ac\to\Delta=4^2-4(-9)(9)=16+324=340\\\\x=(-b\pm\sqrt\Delta)/(2a)\\\\\sqrt\Delta=√(340)=√(4*85)=2√(85)\\\\x=(-4\pm2√(85))/(2(-9))=(2\pm√(85))/(9)\\\\x_1\approx1.25\ and\ x_2\approx0.8`