Question

If (n - k) is a factor of the polynomials
x2 + px +9 & x2 + mx + n. The value of k is​

Answer 1

Answer:

here's your answer

Step-by-step explanation:

Given :

(x+a) is a factor of x

2

+px+q and x

2

+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)

⇒a

2

−ap+q=0⟶(2)

and

(−a)

2

+m(−a)+n=0⟶(3)

⇒a

2

−ma+n=0⟶(4)

Subtracting (2) & (4) we get

−ap+am+q−n=0

⇒+a(m−p)=n−q

⇒a=

m−p

n−q

Hence, proved