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3 years ago

Consider that the roots of a cubic equation with integral coefficients are 2, −1, and 4. Which choice is the cubic equation?

Mathematics

1 answer:

Marina86 [1]3 years ago

6 0

The cubic equation having roots 2, -1 and 4 is $x^3-5x^2+2x+8$

Step-by-step explanation:

The roots of the cubic equation are 2,-1 and 4. We need to find the cubic equation.

If 2,-1 and 4 are roots then:

x=2, x=-1 and x=4

or we can write:

x-2=0, x+1=0 and x-4=0

Multiplying the roots to find the cubic equation:

$(x-2)(x+1)(x-4)\\=(x-2)(x(x-4)+1(x-4))\\=(x-2)(x^2-4x+x-4)\\=(x-2)(x^2-3x-4)\\=x(x^2-3x-4)-2(x^2-3x-4)\\=x^3-3x^2-4x-2x^2+6x+8\\Combining\,\,like\,\,terms:\\=x^3-3x^2-2x^2-4x+6x+8\\=x^3-5x^2+2x+8$

So, the cubic equation having roots 2, -1 and 4 is $x^3-5x^2+2x+8$

Keywords: Solving Cubic Polynomial

Learn more about Solving Cubic Polynomial at:

#learnwithBrainly

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Answer:

Step-by-step explanation:

Factor out to simplify:

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3 years ago

Select all the correct answers.

fenix001 [56]

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Let be f(x) = - 2 · cos (x - 1) + 3, then we use the concept of horizontal translation 4 units in the + x direction:

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Now we apply a reflection over the x-axis:

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2 years ago

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2 years ago

What is the constant term of the quotient when 2x^3-3x^2 + 4x-2 is divided by x^2-x+2?

AlladinOne [14]

Answer:

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Step-by-step explanation:

See the attachment for the polynomial long division. The constant in the quotient is -1.

_____

Here, there is a remainder of -x. If there were no remainder the constant in the quotient is the ratio of the constant in the dividend to the constant in the divisor: -2/2 = -1.

That could be a first guess in a "guess and check" solution approach.

Guess: first term of binomial quotient is (2x^3)/x^2 = 2x; last term of binomial quotient is -2/2 = -1. So, the quotient is guessed to be (2x -1).

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3 years ago