Math, asked by Sham83241, 11 months ago

Find the roots of m4-m3-9m2-11m-4=0

Answers

Answered by ashishks1912
0

The roots of the given equation m^4-m^3-9m^2-11m-4=0 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 m^4-m^3-9m^2-11m-4=0

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 m^3-2m^2-7m-4=0

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 m^2-3m-4=0

Factorise the quadratic equation we get

m^2+m-4m-4=0

m(m+1)-4(m+1)=0

(m+1)(m-4)=0

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

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