Find the roots of the polynomial: f(x)=x^{4}+4x^{2}-32

Adela Brown 2021-12-18 Answered
Find the roots of the polynomial: f(x)=x4+4x232
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Expert Answer

lalilulelo2k3eq
Answered 2021-12-19 Author has 38 answers
Step 1
We have to find the roots of polynomial:
f(x)=x4+4x232
To find the roots of given polynomial we need to put that polynomial equals to zero.
Therefore,
f(x)=0
x4+4x232=0
Solving by factorization method,
x4+8x24x232=0
x2(x2+8)4(x2+8)=0
(x2+8)(x24)=0
Step 2
Either,
x2+8=0
x2=8
x=±8
=±8i (since i=1, imaginary unit)
=±22i
=22i,22i
or,
x24=0
x2=4
x=±4
=±2
=2, -2
Hence, roots of the polynomial are x=22i,2,2,22i.

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Dawn Neal
Answered 2021-12-20 Author has 35 answers
Step 1
Explanation:
Given that,
f(x)=x4+4x232
Let us suppose
x2=u
Function becomes
u2+4u32
Step 2
Now factorize the quadratic
u2+4u32
(u+8)(u-4)
Recall the value of u
(x2+8)(x24)
Further, factorize the (x24)=(x2)(x+2)
We get,
f(x)=(x2+8)(x2)(x+2)

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