Question

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

Polynomial factorization
ANSWERED
asked 2021-03-06
Linear Factorization of \(\displaystyle{x}^{{4}}+{x}^{{3}}+{5}{x}-{10}\)

Answers (1)

2021-03-07
Step 1
Given quartic equation is :
\(\displaystyle{x}^{{4}}+{x}^{{3}}+{5}{x}-{10}={0}\)
Let us first take x common,
\(\displaystyle{x}^{{4}}+{x}^{{3}}+{5}{x}−{10}={0}\)
\(\displaystyle\Rightarrow{x}{\left({x}^{{3}}+{x}^{{2}}+{5}\right)}−{10}={0}\)
\(\displaystyle\Rightarrow{x}{\left({x}^{{3}}+{x}^{{2}}+{5}\right)}={10}\)
\(\displaystyle\Rightarrow{x}={10},{\left({x}^{{3}}+{x}^{{2}}+{5}\right)}={10}\)
Step 2
Now,
\(\displaystyle{x}^{{3}}+{x}^{{2}}+{5}={10}\)
\(\displaystyle\Rightarrow{x}^{{2}}{\left({x}+{1}\right)}={5}\)
\(\displaystyle\Rightarrow{x}^{{2}}={5},{\left({x}+{1}\right)}={5}\)
Again,
\(\displaystyle{x}^{{2}}={5}\)
\(\displaystyle\Rightarrow{x}=\pm{5}{i}\)
and , x+1=5
\(\displaystyle\Rightarrow{x}={4}\)
Step 3
The roots are : \(\displaystyle{10},{4},\pm{5}{i}\)
0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours
...