How do you find all zeros of the function $F (x) = 2 x^{3} - 14 x^{2} - 56 x - 40$ $F(x)=2x^3-14x^2-56x-40$ given 10 as a zero?

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How do you find all zeros of the function $F (x) = 2 x^{3} - 14 x^{2} - 56 x - 40$ $F(x)=2x^3-14x^2-56x-40$ given 10 as a zero?

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Answer 1 · 2016-11-02T18:48:36

The other two zeros are $- 1$ $-1$ and $- 2$ $-2$

Explanation:

Since we are told that $10$ $10$ is a zero, $(x - 10)$ $(x-10)$ must be a factor:

$F (x) = 2 x^{3} - 14 x^{2} - 56 x - 40$ $F(x) = 2x^3-14x^2-56x-40$

$F (x) = (x - 10) (2 x^{2} + 6 x + 4)$ $color(white)(F(x)) = (x-10)(2x^2+6x+4)$

$F (x) = 2 (x - 10) (x^{2} + 3 x + 2)$ $color(white)(F(x)) = 2(x-10)(x^2+3x+2)$

$F (x) = 2 (x - 10) (x + 2) (x + 1)$ $color(white)(F(x)) = 2(x-10)(x+2)(x+1)$

So the other two zeros are $x = - 2$ $x=-2$ and $x = - 1$ $x=-1$

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How do you find all zeros of the function $F (x) = 2 x^{3} - 14 x^{2} - 56 x - 40$ $F(x)=2x^3-14x^2-56x-40$ given 10 as a zero?

1 Answer

Explanation:

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Science

Math

Humanities

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How do you find all zeros of the function F(x)=2x3−14x2−56x−40F(x)=2x^3-14x^2-56x-40 given 10 as a zero?

1 Answer

Explanation:

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How do you find all zeros of the function $F (x) = 2 x^{3} - 14 x^{2} - 56 x - 40$ $F(x)=2x^3-14x^2-56x-40$ given 10 as a zero?