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DaniilM [7]
3 years ago
9

What is the remainder when you divide 2x3 + 4x2 - x + 3 by x + 2?

Mathematics
2 answers:
velikii [3]3 years ago
7 0
<h3><u>The quotient is 2x^2 - 1 + (5/(x + 2))</u></h3><h3><u>The remainder is 5.</u></h3>

Illusion [34]3 years ago
3 0

Answer:  The required remainder is 5.

Step-by-step explanation:  We are given to find the remainder when we divide the following cubic polynomial by (x+2) :

f(x)=2x^3+4x^2-x+3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

We have the following theorem :

<em><u>Remainder theorem : </u></em>  If a polynomial p(x) is divided by the factor (x-a), then the remainder is p(a).

So, for the given linear factor, we have

x+2=0\\\\\Rightarrow x=-2.

Substituting x = -2 in equation (i), we get

f(-2)\\\\=2(-2)^3+4(-2)^2-(-2)+3\\\\=-16+16+2+3\\\\=5.

Thus, the required remainder is 5.

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Let's look into the solution step by step.

Explanation:

Given: A quadratic equation, kx2 - 14x + 8 = 0

Let the two zeros of the equation be α and β.

According to the given question, if one of the roots is α the other root will be 6α.

Thus, β = 6α

Hence, the two zeros are α and 6α.

We know that for a given quadratic equation ax2 + bx + c = 0

The sum of the zeros is expressed as,

α + β = - b / a

The product of the zeros is expressed as,

αβ = c / a

For the given quadratic equation kx2 - 14x + 8 = 0,

a = k, b = -14, c = 8

The sum of the zeros is:

α + 6α = 14 / k [Since the two zeros are α and 6α]

⇒ 7α = 14 / k

⇒ α = 2 / k --------------- (1)

The product of the zeros is:

⇒ α × 6α = 8 / k [Since the two zeros are α and 6α]

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⇒ 6 (2 / k)2 = 8 / k [From (1)]

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⇒ k = 24 / 8

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