The standard way is THIS:
1. Introduce new variable u = x^2. Then your original polynomial takes the form
q(u) = 2u^2 - 5u - 7.
2. Find its zeroes. For it, use the quadratic formula
= = = = .
---> = = , = -1.
3. So, the decomposition for q(u) is
q(u) = 2u^2 - 5u - 7 = 2(u-(7/2))*(u-(-1)) = (2u-7)*(u+1).
Therefore, the decomposition for the original polynomial is
p(x) = 2x^4 - 5x^2 - 7 = (2x^2-7)*(x^2+1).
You may factor it further
p(x) = , if you want.
You can put this solution on YOUR website!
make the substitutions:
and
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Use the quadratic formula
and
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and
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These are the 4 answers, 2 of which are imaginary
You can check them by plugging into given equation
Here's the plot:
Looks close since