Select the approximate values of x that are solutions to f(x) = 0, where f(x) = -9x2 + 7x + 8.

Question

please answer this

Answer 1

-9x^2 + 7x + 8 = 0

Note:  One way to figure these out when they don't factor nicely is to use something called the quadratic formula.  It works like this:

If you have an equation that looks like this:  ax^2 + bx + c = 0

Then x = this:

x = (-b +- sqrt( b^2 - 4ac ) ) / 2a

For this problem a = -9, b = 7, and c = 8.

Plug those into the formula and you get this:

x = (-7 +- sqrt(49-4*-9*8))/2(-9)

x = (-7 +- sqrt(49+288))/-18

x = (-7 +- sqrt(337))/-18

The square root of 324 is 18 and the square root of 361 is 19.  337 is closer to 18, so let's approximate sqrt(337) as 18.

x = (-7 +- 18)/-18

x = -25/-18, 11/-18

x = 25/18, -11/18