Finding roots of the fourth degree polynomial: \(\displaystyle{2}{x}^{{4}}+{3}{x}^{{3}}-{11}{x}^{{2}}-{9}{x}+{15}={0}\)

Braden Hatfield

Braden Hatfield

Answered question

2022-04-06

Finding roots of the fourth degree polynomial:
2x4+3x311x29x+15=0

Answer & Explanation

rhyclelal80j6

rhyclelal80j6

Beginner2022-04-07Added 13 answers

First notice that x=1 gives 0. So x1 is a factor.
Next rewrite as
2x42x3+5x35x26x2+6x15x+15
This is to try and get x1 as a factor.
This gives us
2x3(x1)+5x2(x1)6x(x1)15(x1)=(x1)(2x3+5x26x15)
Now notice that 2x36x=2x(x23) and 5x215=5(x23)
Thus
(x1)(2x3+5x26x15)=(x1)(2x(x23)+5(x23))=(x1)(x23)(2x+5)
and so the roots are 1,±3,52

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