Question

Find all the zeros of f(x) = 2x^4 − 5x^3 − 5x^2 + 20x − 12

Answer 1

x=-2 x=2 x = 1/2 x=3

Explanation:

f(x) = 2x^4 − 5x^3 − 5x^2 + 20x − 12

Graph

We see that there is a zero at -2

Using synthetic division

-2 2 -5 -5 20 -12

-4 18 -26 12

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2 -9 13 -6 0

This gives us ( x+2) ( 2x^3 -9x^2 +13x -6)

We see that there is a zero at 2

Using synthetic division ( 2x^3 -9x^2 +13x -6)

2 2 -9 13 -6

4 -10 6

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2 -5 3 0

This gives us ( x+2) ( x-2) ( 2x^2 -5x+3)

We can factor ( 2x^2 -5x+3)

( x+2) ( x-2) ( 2x -1) ( x-3)

Using the zero product property

( x+2)=0 ( x-2)=0 ( 2x -1)=0 ( x-3)=0

x=-2 x=2 x = 1/2 x=3