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Reil [10]
3 years ago
13

Find k if (x+1) 2x^3+kx^2+1

Mathematics
1 answer:
Viktor [21]3 years ago
3 0
<h2>Question:</h2>

Find k if (x+1) is a factor of 2x³ + kx² + 1

<h2>Answer:</h2>

k = 1

<h2>Step-by-step explanation:</h2>

The factor of a polynomial F(x) is another polynomial that divides evenly into F(x). For example, x + 3 is a factor of the polynomial x² - 9.

<em>This is because;</em>

i. x² - 9 can be written as (x - 3)(x + 3) which shows that both (x - 3) and (x + 3) are factors.

ii. If x = -3 is substituted into the polynomial x² - 9, the result gives zero. i.e

=> (-3)² - 9

=> (9) - 9 = 0

Therefore, if (x + a) is a factor of a polynomial, substituting x = -a into the polynomial should result to zero. This also means that, if x - a is a factor of a polynomial, substituting x = a into the polynomial should give zero.

<em><u>From the question</u></em>

Given polynomial: 2x³ + kx² + 1

Given factor: x + 1.

Since x + 1 is a factor of the polynomial, substituting x = -1 into the polynomial should give zero and from there we can calculate the value of k. i.e

2(-1)³ + k(-1)² + 1 = 0

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

-2 + k + 1 = 0

k - 1 = 0

k = 1

Therefore the value of k is 1.

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3 years ago
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oksano4ka [1.4K]

Answer:

c = 5√5

Step-by-step explanation:

When we have a right triangle, there is a property about its measurements that is <em>always</em> true, and its called the "Pythagorean Theorem"

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we can call one leg "a", the other leg "b" and the slanted side "c"

("c" is also called the hypotenuse--and it's always opposite the 90-degree angle)

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let's try plugging these values into our formula:

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now, we know what c² is--but we want to know c,

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now, while √125 <em>is </em>our answer, we can simplify further!

this is because 125 can be made up of 5 · 25

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we can take out the square root of 25 (5):

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so, in simplest radical form, c = 5√5

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hope this helps!! have a lovely day :)

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