Question

If (x + p) is the HCF of (x² + bx + a) and (x² + cx + d), then find the value of p.

a)d-a/b-c
b)b-c/c-d
c)b+c/c+d
d)d+a/b+c
e)ab/cd​

Answer 1

Answer: a)d-a/b-c

Given x+k is HCF of x2+ax+b and x2+cx+d

Therefore x+k is a factor of each expression.

Put x=−k is the given expressions.

(−k)2+(a)(−k)+b=0

⇒k2−ka+b=0 ………(1)

also (−k)2+c(−k)+d=0

⇒k2−ck+d=0 …..(2)

substract equation (2) from (1)

c.k−a.k−d+b=0

k(c−a)=d−b

⇒k=c−ad−b.