Question

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

Answer 1

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

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