Question

find zeroes of the polynomial x⁴+3x³-7x²-27x-18​

Answer 1

Answer:

If  α and  B  are two roots of  f(x)  then  (x−α)  and  (x−B)  are two factors of the given polynomial.

Thus,  (x−α)(x−β)=(x+3–√)(x−3–√)=x2−3  divides  f(x).  

x4−3x3−x2+9x−6x2−3  

=x2−3x+2  (by division method).

Now, only task remained is to factorise  x2−3x+2.  

x2−3x+2=(x−1)(x−2).  

Therefore, other roots are :

x=1  and  x=2.

Hope this help you ;

Bhavy Yadav