What are all of the real roots of the following polynomial? f(x) x^4-24x^2-25
2 answers:
Answer:
The real roots are ±5
Step-by-step explanation:
It is given that,
f(x) = x^4 - 24x^2 - 25
<u>To find the real roots</u>
Let x^4 - 24x^2 - 25 = 0 ----(1)
Take y = x^2
Then eq (1) becomes,
y^2 - 24y - 25 = 0
By using splitting method we can write,
y^2 + y - 25y - 25 = 0
y(y + 1) - 25(y +1) = 0
(y + 1)(y - 25) = 0
(x^2 + 1 )(x^2 - 25) = 0
From (x^2 + 1 ) we get complex roots
x^2 = -1
x = √-1
x - 25 = 0 we get real roots
x = 25
x = ±5
Therefore the real roots are ±5
<u>Answer:</u>
x = ±5
<u>Step-by-step explanation:</u>
We are given the following polynomial function and we are to find all of its real roots:

Let
so we can now write it as:

Factorizing it to get:



Substitute back
to get:

The quadratic factor has only complex roots. Therefore, the real roots are x = ±5.
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