How do I find the roots for the quartic: 2x^4 + 3x^3 + 7x^2 – 7x – 5?
^ = to the power of
I have a trigonometry/algebra II review test tomorrow and these types of problems are the only ones I don’t understand on my study guide. I’m simply supposed to find the four roots of the equation (imaginary or real), but I can’t figure it out! I have tried factoring, but I don’t know how to do it with quartic equations. Please answer with a simple method, I haven’t learned any of the special equations for solving quartics.
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f(x) = 2x^4 + 3x^3 + 7x^2 – 7x – 5 = 0.
By trial and error,
f(1)= 2+3+7-7-5 = 0
Therefore, (x-1) is one of the roots,
f(x) = (x-1)(2x^3 + 5x^2 +12x +5) = 0
Again, by trial and error,
f(-0.5)= (-1.5)(-0.25+ 1.25-6+5)= 0
Therefore, (2x+1) is another roots,
Now, you can see that x^2 + 2x +5 cannot be factored, that means they are imaginary. But you should be able to solve them now.
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