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

1 Answer
Nov 1, 2016

Answer:

Yes

Explanation:

#f(x) = 4x^4+9x^2+9x+2 = ((4x^2+9)x+9)x + 2#

So

#f(color(blue)(-1/2)) = ((4(color(blue)(-1/2))^2+9)(color(blue)(-1/2))+9)(color(blue)(-1/2))+2#

#color(white)(f(color(white)(-1/2))) = ((1+9)(color(blue)(-1/2))+9)(color(blue)(-1/2))+2#

#color(white)(f(color(white)(-1/2))) = (-5+9)(color(blue)(-1/2))+2#

#color(white)(f(color(white)(-1/2))) = -2+2#

#color(white)(f(color(white)(-1/2))) = 0#

Yes, #f(-1/2) = 0#