Answered

Connect with a community that values knowledge and expertise on IDNLearn.com. Ask your questions and receive comprehensive and trustworthy answers from our experienced community of professionals.

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

Sagot :

[tex]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=\frac{-b\pm\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{340}=\sqrt{4\times85}=2\sqrt{85}\\\\x=\frac{-4\pm2\sqrt{85}}{2(-9)}=\frac{2\pm\sqrt{85}}{9}\\\\x_1\approx1.25\ and\ x_2\approx0.8[/tex]
Kate200468idn
[tex]f(x) = -9x^2 + 4x + 9\ \ \ and\ \ \ f(x)=0\\\\-9x^2 + 4x + 9=0\ \ \ \Leftrightarrow\ \ \ 9x^2 - 4x + \frac{4}{9} -\frac{4}{9}- 9=0\\\\(3x-\frac{2}{3})^2=9\frac{4}{9}\ \ \ \Leftrightarrow\ \ \ (3x-\frac{2}{3})^2= \frac{85}{9} \\\\3x-\frac{2}{3}= \frac{ \sqrt{85} }{3} \ \ \ or\ \ \ \ \ \ 3x-\frac{2}{3}= -\frac{ \sqrt{85} }{3}\\\\3x= \frac{2+ \sqrt{85} }{3} \ \ \ \ \ \ or\ \ \ \ \ \ 3x= \frac{2- \sqrt{85} }{3}\\\\ x= \frac{2+ \sqrt{85} }{9} \ \ \ \ \ \ \ \ or\ \ \ \ \ \ \ x= \frac{2- \sqrt{85} }{9}\\\\[/tex]

[tex]x\approx1.247\ \ \ \ \ \ \ \ or\ \ \ \ \ \ \ x\approx-0.802[/tex]
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Your questions deserve accurate answers. Thank you for visiting IDNLearn.com, and see you again for more solutions.