What are the roots of the polynomial equation x3 - 10x=-3x2+ 24? Please help

Mathematics

2 answers:

snow_tiger [21]3 years ago

7 0

Answer:

x = -2, 3, -4.

Step-by-step explanation:

x^3 - 10x = -3x2 + 24 = 0

x^3 + 3x^2 - 10x - 24 = 0

The last term is 24 and the coefficient of x^3 is 1 so +/- 1, +-2, +/- 3 and +/- 4 could be among the roots ( by The Rational Root Theorem).

Let x = 1

f(x) = 1^3 +3(1)^2 - 10 - 24 = -30 so it's no t .

f(-1) = -1 + 3 + 10 - 24 = -12 so it's not -1.

Let x = 2:

f(2) = 2^3 +3*4 - 20 - 24 = -32 so its not 2

f(-2) = -8 + 12 + 20 - 24 = 0 so x = -2 is a root

and therefore x+ 2 is a factor and we divide:

x + 2 ) x^3 + 3x^2 - 10x - 24 ( x^2 + x - 12 <------ The quotient

x^3 + 2x^2

x^2 - 10x

x^2 + 2x

-12x - 24

..............

Now x^2 + x - 12 = (x - 3)(x + 4)

So (x + 2)(x - 3)(x + 4) = 0

This gives

x = -2, 3, -4.

Serggg [28]3 years ago

7 0

Answer:

–4, –2, and 3

Step-by-step explanation:

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Tresset [83]

By definition, two angles are supplementary if the sum of them is 180 degrees. In this case (see figure attached with the answer) the line AD is transversal to lines AB and DC. This is a proof of the Same-side interior angle theorem.

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By the definition of a parallelogram, AB∥DC. AD is a transversal between these sides, so ∠A and ∠D are same-side interior angles. Because AB and DC are parallel, the same-side interior angles must be supplementary by the same-side interior angles theorem. Therefore, ∠A and ∠D are supplementary.