Select the approximate values of x that are solutions to f(x)=0, where f(x)=-2x^2+9x+9

Question

Select the approximate values of x that are solutions to f(x)=0, where f(x)=-2x²+9x+9

 

A. {0.22, 1.00}

B. {-2, 9}

C. {-4.50, -4.50}

D. {-0.84, 5.34}

Answer 1

-2x² + 9x + 9 = 0

 

All of these problems work the same way, Trisha.  You should try a few of them on your own.  To find the values of x that cause f(x) to equal 0, apply the quadratic formula:

 

x = [-b ± √(b²-4ac)]/(2a)

 

Where a is the coefficient of the x² term (-2), b is the coefficient of the x term (+9) and c is the constant term (+9):

 

x = [-9 ± √(9²-4(-2)(9))]/(-4)

 

x = [-9 ± 3√17]/(-4)

 

Now 3√17 ≅ 12.37

 

x ≅ (-9 ± 12.37)/(-4)

 

Can you finish from here?

Answer 2

Hey Trisha, 

We can complete the square which always works:

 

-2x² + 9x + 9 = 0 

 2x²   - 9x  - 9 = 0 

  x²  - 9x/2  = 9/2  

 (x - 9/4)² = 9/2 + 81/16

 x - 9/4 = ±√(9/2   + 81/16)

 

 x = 9/4 + √(9/2 + 81/16) = 5.34

or 

 x = 9/4  - √(9/2 + 81/16) = -0.84

 

I hope this helps.