Question

how can you find the roots of this polynomial equation:2x^4-7x^#+21x^2+17x-13?

Answer 1

That's a monster!

Answer 2

First check if \(2\) is a root.

Answer 3

Check \(1, -1, 2, -2\) and pray one of them is a root.

Answer 4

If one of them is a root then divide out \(x-\text{root}\)

Answer 5

I think you're supposed to use factorization.

Answer 6

If you see how to do that @wolfgirl then show how.

Answer 7

i did use syntethetic division and use -1 and 1/2 as the divisor then after that i get the answer 2x^2-8x+26 then since i couldny use factorixation then i use quadratic formula and my answers turn out to be 10sqrtof11all over 4 and 6sqrt of 11 all over 4

Answer 8

and the problem is idki if thats was correct ill appreciate if youll tell me my errors

Answer 9

Show your work

Answer 10

Square both sides:
2 x^4-7 x^3+21 x^2+17 x-13 = 0
The left hand side factors into a product with three terms:
(x+1) (2 x-1) (x^2-4 x+13) = 0

I think you can do the rest. Btw, I'm not Wolfgirl :)

Answer 11

Also, you made a mistake in the question with that #. I know from chat though you meant 3

Answer 12

Don't check 2 or -2.

The Rational Root Theorem suggests +/- 1, +/- 1/2, +/- 13, and +/- 13/2

By your result, you had hits on x = -1 and x = 1/2.

Answer 13

@tkhunny so is my results correct?

Answer 14

Typically, I would prefer (2x-1) in the place of (x-1/2), but other than that it seems fine.