Question

If n-K) is
factor of the
polynomial (x²+ Px+q +m)show that k=n+(n+p/m-p) ​

Answer 1

Step-by-step explanation:

Given :

(x+a) is a factor of x2+px+q and x2+mx+n

then using the factor theorem which says that the polynomial f(x0 has a factor (x−k) if and only if f(k)=0

We have

(−a)2+p(−a)+q=0⟶(1)

⇒a2−ap+q=0⟶(2)

and

(−a)2+m(−a)+n=0⟶(3)

⇒a2−ma+n=0⟶(4)

Subtracting (2) & (4) we get

−ap+am+q−n=0

⇒+a(m−p)=n−q

⇒a=m−pn−q

                                    

Hence, proved