Question

Find all roots of 2(x)^3+3(x)^2-5x-7=0
Find all roots of 2(x)^3+3(x)^2-5x-7=0
@Mathematics

Answer 1

Doesn't look factorable, .. can try fundamental theorem of algebra and related theorem along with synthetic division to track one of the roots, then use quadratic formula to get the other 2.

Answer 2

Can you pl help me some more?

Answer 3

I am not able to find the solution

thanks in advance

Answer 4

Try evaluating at x=1 and at x=-1 first, then you'll have 3 points to graph (0,-7) is free.
Look at the graph and it'll point you to where the roots are likely hiding.

Answer 5

i want to find them algebrically

Answer 6

Are you familiar with the following theorems, and do you know how to do synthetic division?
-Fundamental Theorem of Algebra
-Descartes' Rule of Signs
-Rational Root Theorem
-Factor-root theorem / remainder theorem

?

Answer 7

yes
i do know these theorems

Answer 8

FTA tells us that the polynomial has 3 roots.
DRS shows that (evaluating at x=1), there is one sign change among the terms, so there is one real root. (evaluating at x=-1), there two sign changes, so there are either 2 real roots, or 2 complex roots.

Answer 9

okay

Answer 10

The Rat. Root Th'm shows that if there are rational roots, they will occur at +- 7/2, 1
+- 1 was already checked, so the next one to try is 7/2. We are guaranteed exactly one positive real root, so try +7/2 first. Use synthetic division or just evaluate the function at x=7/2 to check.

Answer 11

alright

Answer 12

Oops, forgot in the DRS comment that there will be one *positive* real root and 2 or 0 *negative* real roots.

Answer 13

its okay

Answer 14

pl CliffSedge can you help me solve this problem
?

Answer 15

I'll assume you've tried evaluating at all the possible rational roots and have found that there are no rational roots. In that case, things get a bit trickier. From the graph, all 3 roots are real numbers, but they are not rational.

Answer 16

okay

Answer 17

There is such a thing as the Cubic Formula, similar to the Quadratic Formula, but it's a real beast to use.

Answer 18

i do know that

Answer 19

i thought may be some can solve it in an easier way

Answer 20

Anyways
thanks a lot for your help

Answer 21

That's a real tricky one you got there. Maybe approximate roots using techniques from calculus?

Answer 22

okay
thank you once again

Answer 23

http://www.wolframalpha.com/input/?i=2%28x%29^3%2B3%28x%29^2-5x-7%3D0

Looks like it has no integer or fractional solutions, algebra is hardly helpful in this problem