Question

solve this queation plzz ​

Answer 1

Step-by-step explanation:

Given:-

If x+a is a factor of the polynomial and x²+px+q

and x²+mx+n

To prove:-

a=(n-q)/(m-p)

Solution:-

Given polynomials are p(x)=x²+px+q

and g(x)=x²+mx+n

Given factor=x+a

We know that

If (x-a) is a factor of p(x) then p(a)=0

now,

x+a is a factor then p(-a)=0 and g(-a)=0

p(-a)=(-a)²+p(-a)+q=0

=>p(-a)=a²-pa+q=0

=>a²=pa-q-----(1)

g(-a)=(-a)²+m(-a)+n=0

=>g(-a)=a²-ma+n=0

=> a²=ma-n----(2)

From (1)&(2)

pa-q=ma-n

=>pa-ma=q-n

=>a(p-m)=q-n

=>a(m-p)=n-q

=>a=(n-q)/(m-p)

Answer:-

a=(n-q)/(m-p)

Proved the given relation

Answer 2

Answer:

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