Quadratic functions

Question

The function f(x) = -4x + 15 includes a polynomial of degree 1 and has 1 root

Use inverse operations to solve -4x + 15 = 0

 

The function f(x) = x² - 8x + 15 includes a polynomial of degree 2 and has 2 roots.

Use factoring to solve x² - 8x + 15 = 0

 

The function f(x) = x² - 8x + 20mincludes a polynomial of degree 2 and has 2 roots.

Use the Quadratic Formula to solve x² - 8x + 20 = 0

 

The function f(x) = x³ - 4x² - 4x + 16 includes a polynomial of degree 3 and has 3 roots.

Use your graphing calculator to solve x³ - 4x² - 4x + 16 = 0

Answer 1

DO operations are multiply by -4 then add 15.

UNDO operations are subtract 15 then divide by -4:

Start with zero, subtract 15 to get -15. Now divide -15 by -4 to get 15/4, so this is the value of x.

x²-8x+15=(x-3)(x-5) making the roots 3 and 5.

x²-8x+20=0; x=(8±√64-80)/2=4±√-16/2=4±2i. Roots are complex 4+2i and 4-2i.

x³-4x²-4x+16=0=x²(x-4)-4(x-4)=(x²-4)(x-4)=(x-2)(x+2)(x-4) making the roots -2, 2, 4.