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Given the function f(x) = x3 - 2x2 - 19x + 20, the zeros of the function are

User Rahpuser
by
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1 Answer

9 votes

Answer:

-4, 1, and 5

Explanation:

To find the zeros of a polynomial, I like to get rid of the x's and keep the coefficients like this: x³ - 2x² - 19x + 20 -> 1 -2 -19 20

Now, we do some long division, let's try it out

For every number on the third row, multiply by it by the 1 and carry it over

1 | 1 -2 -19 20

0

1

Multiply the first coefficient by 1 and add it to the second coefficient

1 | 1 -2 -19 20

0 1

1 -1

Multiply the second coefficient by 1 and add it to the third coefficient

1 | 1 -2 -19 20

0 1 -1

1 -1 -20

I think you get the idea

1 | 1 -2 -19 20

0 1 -1 -20

1 -1 -20 0

We end up with a remainder of 0, meaning 1 is one of the zeros

Usually, you would just plug and test, but I'll save you some time and spoil the fun for you; the remaining zeros are -4 and 5

-4 | 1 -1 -20

0 -4 20

1 -5 0

5 | 1 -5

0 5

0 0

User Jdm
by
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