Is -1/2 a zero of the polynomial $f (x) = 4 x^{4} + 9 x^{2} + 9 x + 2$ $f(x)=4x^4+9x^2+9x+2$ ?

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Is -1/2 a zero of the polynomial $f (x) = 4 x^{4} + 9 x^{2} + 9 x + 2$ $f(x)=4x^4+9x^2+9x+2$ ?

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Answer 1 · 2016-11-01T07:10:42

Yes

Explanation:

$f (x) = 4 x^{4} + 9 x^{2} + 9 x + 2 = ((4 x^{2} + 9) x + 9) x + 2$ $f(x) = 4x^4+9x^2+9x+2 = ((4x^2+9)x+9)x + 2$

So

$f (- \frac{1}{2}) = ((4 {(- \frac{1}{2})}^{2} + 9) (- \frac{1}{2}) + 9) (- \frac{1}{2}) + 2$ $f(color(blue)(-1/2)) = ((4(color(blue)(-1/2))^2+9)(color(blue)(-1/2))+9)(color(blue)(-1/2))+2$

$f (- \frac{1}{2}) = ((1 + 9) (- \frac{1}{2}) + 9) (- \frac{1}{2}) + 2$ $color(white)(f(color(white)(-1/2))) = ((1+9)(color(blue)(-1/2))+9)(color(blue)(-1/2))+2$

$f (- \frac{1}{2}) = (- 5 + 9) (- \frac{1}{2}) + 2$ $color(white)(f(color(white)(-1/2))) = (-5+9)(color(blue)(-1/2))+2$

$f (- \frac{1}{2}) = - 2 + 2$ $color(white)(f(color(white)(-1/2))) = -2+2$

$f (- \frac{1}{2}) = 0$ $color(white)(f(color(white)(-1/2))) = 0$

Yes, $f (- \frac{1}{2}) = 0$ $f(-1/2) = 0$

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Is -1/2 a zero of the polynomial $f (x) = 4 x^{4} + 9 x^{2} + 9 x + 2$ $f(x)=4x^4+9x^2+9x+2$ ?

1 Answer

Explanation:

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Is -1/2 a zero of the polynomial f(x)=4x4+9x2+9x+2f(x)=4x^4+9x^2+9x+2?

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Explanation:

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Is -1/2 a zero of the polynomial $f (x) = 4 x^{4} + 9 x^{2} + 9 x + 2$ $f(x)=4x^4+9x^2+9x+2$ ?