Question

determine the rational roots of 2x^5-11x^4+14x^3-2x^2+12x+9=0

Answer 1

Hi,

The first 3 roots are -.5, 3, and 3.
. .____________________
-.5)2 . -11 . 14 . -2 . 12 . 9
. ____ -1__ 6_-10__ 6_-9_
. .2 . .-12 . 20 -12 . 18 . 0
.__________________
3).2 . .-12 . 20 -12 . 18
._____ 6_-18__ 6_-18_
. .2 . . -6 . .2 . .-6 . .0
. _______________
3) .2 . -6 . .2 . .-6
. ____6__ 0___6_
. . 2 . .0 . . 2 . . 0

2x² + 2 = 0

2x² = -2

x² = -1
. . . . .__
x = ±√-1

x = ±i, -.5, 3, and 3 <==ANSWER

I hope that helps!! :-)

Answer 2

@adinarayan thank you!!!

Answer 3

\[2 x^5-11 x^4+14 x^3-2 x^2+12 x+9=(x-3)^2 (2 x+1) \left(x^2+1\right) \]