Question

If (x+a) is a factor of two polynomials x2+px+q and x2+mx+n, then prove that : a=n- q/m-p​

Answer 1

Answer:

Step-by-step explanation:

Please refer to given attachment

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Answer 2

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

Step-by-step explanation:

Let, p(x) = x² + px + q

P(x) = x² + mx + n

As (x + a) is a factor of the given polynomials, both must be zero for x = -a.   Using factor theorem:

If x - a is factor: p(x) = 0

=> a² + p(a) + q = 0

=> a² = - q - ap ...(1)

If x - a is factor: P(x) = 0

=> a² + m(a) + n= 0

=> a² = - n - am ...(2)

Compare (1) and (2) :

=> - q - ap = - n - am

=> n - q = ap - am

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

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