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Reika [66]
3 years ago
10

If a polynomial function f(x) has roots 0, 4, and 3+ /11, what must also be a root of f(x)?

Mathematics
1 answer:
seropon [69]3 years ago
6 0

Answer:

3 - \sqrt{11}

Step-by-step explanation:

Assuming the root given is 3 + \sqrt{11}

Radical roots occur in conjugate pairs, thus

if 3 + \sqrt{11} is a root , then 3 - \sqrt{11} is also a root

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(2x² - 5x-3)/ (x-3)<br> DIvide the polynomials
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Answer:

2x + 1

Step-by-step explanation:

\frac{(2x² - 5x-3)}{(x - 3)}

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<em><u>Or another step</u></em>

Step by Step Solution

STEP

1

:

Equation at the end of step 1

STEP

2

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2x² - 5x - 3/ x - 3

Trying to factor by splitting the middle term

2.1 Factoring 2x² - 5x - 3

The first term is, 2x² its coefficient is 2 .

The middle term is, -5x its coefficient is -5 .

The last term, "the constant", is -3

Step-1 : Multiply the coefficient of the first term by the constant 2 • -3 = -6

Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is -5 .

-6 + 1 = -5 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 1

2x² - 6x + 1x - 3

Step-4 : Add up the first 2 terms, pulling out like factors :

2x • (x-3)

Add up the last 2 terms, pulling out common factors :

1 • (x-3)

Step-5 : Add up the four terms of step 4 :

(2x+1) • (x-3)

Which is the desired factorization

Canceling Out :

2.2 Cancel out (x-3) which appears on both sides of the fraction line.

Final result :

2x + 1

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