Fred's teacher gave the class the
quadratic function f(x) = 4x² + 16x+9
State two different methods Fred could use to solve the equation f(x) = 0.

Using one of the methods stated in part a, solve f(x) = 0 for x, to the nearest
tenth.


Sagot :

Two methods Fred could use to solve the equation are

  1. The completing the square method
  2. The formula method

The solution for the function is x ≅ -0.7 OR x ≅ - 3.3

Solving quadratic equations

From the question, we are to solve the given quadratic equation

Two methods Fred could use to solve the equation are

  1. The completing the square method
  2. The formula method

The given quadratic function is

f(x) = 4x² + 16x+9

Now, we are to solve f(x) = 0 for x

That is,

4x² + 16x+9 = 0

Using the formula method to solve the equation

[tex]x =\frac{-b \pm \sqrt{b^{2}-4ac } }{2a}[/tex]

In the equation,

a = 4, b = 16, and c = 9

∴ [tex]x =\frac{-16 \pm \sqrt{16^{2}-4(4)(9) } }{2(4)}[/tex]

[tex]x =\frac{-16 \pm \sqrt{256-144 } }{8}[/tex]

[tex]x =\frac{-16 \pm \sqrt{112 } }{8}[/tex]

[tex]x =\frac{-16 \pm 10.58 }{8}[/tex]

[tex]x =\frac{-16+ 10.58 }{8}[/tex] OR [tex]x =\frac{-16- 10.58 }{8}[/tex]

[tex]x =\frac{-5.42 }{8}[/tex] OR [tex]x =\frac{-26.58 }{8}[/tex]

x = -0.6771 OR x = - 3.3229

x ≅ -0.7 OR x ≅ - 3.3

Hence, the solution for the function is x ≅ -0.7 OR x ≅ - 3.3

Learn more on Solving quadratic equations here: https://brainly.com/question/8649555

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