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love history [14]
3 years ago
10

Which of the following sets contains all roots of the polynomial f(x)=2x^3+3x^2-3x-2?

Mathematics
1 answer:
svlad2 [7]3 years ago
4 0

Answer:

C

Step-by-step explanation:

Given

f(x) = 2x³ + 3x² - 3x - 2

Note that

f(1) = 2 + 3 - 3 - 2 = 0 , thus

(x - 1) is a factor

Dividing f(x) by (x - 1) gives

f(x) = (x - 1)(2x² + 5x + 2) = (x - 1)(x + 2)(2x + 1)

To find the roots equate f(x) to zero, that is

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

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x + 2 = 0 ⇒ x = - 2

2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - \frac{1}{2}

The solution set is therefore

{ - 2, - \frac{1}{2}, 1 } → C

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Use the figure to the right to find the value of PT. T is the midpoint of PQ.
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Answer:

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Step-by-step explanation:

Given that T is the midpoint of line PQ, segments PT = 5x + 2, and TQ = 7x - 6 that are formed would be equidistant or congruent. PT = TQ.

Therefore:

5x + 2 = 7x - 6

Let's find the value of x

Rearrange the equation, so that the terms having x would be on your left, while those without x would be on your right.

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Divide both sides by -2

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Plug in the value of x into the expression, 5x + 2, to find PT.

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