Question

if (x+1) is a common factor of the polynomial x2+px q and x2+mx+n then find the value of x

Answer 1

Answer:

Step-by-step explanation:

(x + a) is a factor of x2 + px + q

(-a)2 + p(-a) + q = 0

a2 - ap + q = 0 ...(i)

(x + a) is a factor of x2 + mx + n

(-a)2 + m (-a) + n = 0

a2 - am + n = 0 ...(ii)

From (i) and (ii),

-ap + am + q - n = 0

a(m - p) = n - q

a = $\frac{n - q}{m - p}$