What are all of the real roots of the following polynomial? f(x) = x4 - 24x2 - 25
2 answers:
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The factors for given equation f(x)=.
- (x-1) - No
- (x-3) - No
- (x+3) - Yes
- (x-5) - Yes
- (x+5) - Yes
<u>Step-by-step explanation:</u>
The given equation is f(x)= .
Add 0 at the end of the equation.
= 0.
Let us group the given equation,
=0.
⇒ Group 1: .
Group 2: .
Pull out factor from each group,
⇒ Group 1: .
Group 2: (x+3) (-25).
Join the two group since both (x+3) is common in both groups.
=0.
One of the factor is (x+3).
Other factors are solved by the formula, .
= (x+5) (x-5) .
The other factors are (x+5) and (x-5).