Quadratic Equation

Question

Hey! 

 

I need a little help. Could someone give me the first steps so that i can solve this

               

                 

f(x)=(4x−3)²

 

Answer 1

If you are trying to use the quadratic formula to solve -

 

1)  Multiply out    f(x) = (4x-3)² = (4x-3)(4x-3) = 16x²-24x+9

 

2)  You use the quadratic formula to find the point(s) where the graph crosses the x-axis.  That happens when f(x) = 0.

      So 16x² -24x +9 = 0

 

3)  Decide what a, b and c are: 

     a is the coefficient of x², so a = 16

     b is the coefficient of x, so b = -24

     c is the constant term, so c = 9

 

4)  Recall that the quadratic formula is:

     x = -b ± √(b² - ac)  all over 2a

 

5)   Substitute a, b and c into the formula.

     x = [24 ± √(24² - 4(16)(9)) ] / 2(16)

 

        = [24 ± √(576-576)] /32

 

        =  [24 ± √0 ] /32  

 

        = [24 + 0 ] /32   OR   [24 - 0 ] /32

 

        = 24/32 = 3/4 = 0.75

 

Notice that you got the answer 3/4 twice.... once because you added 0 and once because you subtracted 0.

 

The right way to say this is:  3/4 is a repeated root because the discriminant is equal to zero.

 

I hope this helped!