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What are the zeros of the polynomial functionF(x) = x³ + x² - 6x?OA.x = -2, x = 0, and x = 3B. x = -6, x = 0, and x = 1C. x = -1, x = 0, and x = 6OD. x = -3, x = 0, and x = 2

What are the zeros of the polynomial functionFx x x 6xOAx 2 x 0 and x 3B x 6 x 0 and x 1C x 1 x 0 and x 6OD x 3 x 0 and x 2 class=

Respuesta :

Given the polynomial functions:

[tex]F(x)=x^3+x^2-6x[/tex]

We can express this polynomial in factored form:

[tex]F(x)=x(x^2+x-6)[/tex]

But:

[tex]x^2+x-6=(x+3)(x-2)[/tex]

Then:

[tex]F(x)=x(x+3)(x-2)[/tex]

Finally, to find the zeros of the polynomial, we solve the equation:

[tex]x(x+3)(x-2)=0[/tex]

This cubic equation turns into three linear equations:

[tex]\begin{gathered} x=0 \\ x+3=0\Rightarrow x=-3 \\ x-2=0\Rightarrow x=2 \end{gathered}[/tex]

Answer:

[tex]D.\text{ }x=-3,x=0,x=2[/tex]

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