Question

Linear Factorization of x^{4}+x^{3}+5x-10

Polynomial factorization
ANSWERED
asked 2021-05-05
Linear Factorization of \(x^{4}+x^{3}+5x-10\)

Answers (1)

2021-05-06
Step 1
Given quartic equation is :
\(x^{4}+x^{3}+5x-10=0\)
Let us first take x common,
\(x^{4}+x^{3}+5x-10=0\)
\(\Rightarrow x(x^{3}+x^{2}+5)-10=0\)
\(\Rightarrow x(x^{3}+x^{2}+5)=10\)
\(\Rightarrow x=10, (x^{3}+x^{2}+5)=10\)
Step 2
Now,
\(x^{3}+x^{2}+5=10\)
\(\Rightarrow x^{2}(x+1)=5\)
\(\Rightarrow x^{2}=5, (x+1)=5\)
Again,
\(x^{2}=5\)
\(\Rightarrow x = \pm 5i\)
and, x+1=5
\(\Rightarrow x=4\)
Step 3
The roots are : \(10,4 \pm 5i\)
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