Find the roots of m4-m3-9m2-11m-4=0
Answers
The roots of the given equation is m=-1,m=-1,m=-1 and m=4
Therefore the roots are m=-1,-1,-1,4
Step-by-step explanation:
Given equation is
Since the given equation has degree 4 so it must have 4 roots
To find the roots of the given equation :
By using the synthetic division we can find the roots
-1_| 1 -1 -9 -11 -4
0 -1 2 7 4
_____________________
1 -2 -7 -4 0
∴ m+1 is a factor of the given equation
Now for
Again using the synthetic division
-1_| 1 -2 -7 -4
0 -1 3 4
_____________________
1 -3 -4 0
∴ again m+1 is a factor of the given equation
Now we have the quadratic equation
Factorise the quadratic equation we get
Therefore the m+1=0 or m-4=0 are the factors
For the given quadratic equation we have (m+1),(m+1),(m+1),(m-4) are the factors
Now find the roots with these factors we get
m+1=0,m+1=0,m+1=0,m-4=0
m=-1,m=-1,m=-1 and m=4
Therefore the roots are m=-1,-1,-1,4