college algebra

connie3

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Oct 8, 2009
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x^4 -50x^2+49 = 0

I thought I could factor out an x^2, but not I'm lost. Also, their are 4 required answers, where as other problems like this have only been 2 answers. Help please! Thanks!
 


Yup, a fourth-degree polynomial has exactly four roots (always considering multiplicity).

An nth-degree polynomial has exactly n roots.

The key to this exercise is recognizing that the given polynomial is quadratic "in form".

We handle this by making a substitution (at the beginning), and then reversing the substitution (at the end).

Let z = x^2

Now make the substitution.

z^2 - 50z + 49 = 0

This 2nd-degree polynomial equation has exactly two solutions.

After you find them, substitute back.

In other words, set each of the two solutions equal to x^2.

The resulting two equations each have two solutions, giving a total of four solutions to the original equation.

Does that help?

 
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