SOLUTION: Please help me solve this equation. {{{9x^2-17x^4+21x^5}}}

Question 116758This question is from textbook Intermediate Algebra
: Please help me solve this equation. This question is from textbook Intermediate Algebra

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
This is not an equation. This is a polynomial expression. As it stands, there is no solution -- you can't 'solve' a polynomial expression.

So, let's presume that you actually meant to say 'Please solve: .

The first thing you can do is factor out of the left side leaving you with:

That gives us two of the five roots directly, namely and

From here on it gets mighty ugly. Looking at a graph of the cubic factor, we can see that we have one real root, slightly smaller than and a conjugate pair of complex roots.

My recommendation, to the extent that your instructor will be satisfied with a reasonable approximation, is to go to a website that has a general cubic equation solver. When you use such a thing, just be sure to remember that the c coefficient in has a zero value in this problem.

There is another possibility that occurred to me -- you may have a typo in your polynomial. If you actually meant , then becomes:

and we are left with a much easier to handle quadratic.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

The discriminant -467 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

In the field of imaginary numbers, the square root of -467 is + or - .

The solution is

Here's your graph:

Not nearly as messy, even though the roots are complex.

Hope this helps.

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