Question

If x2 + ax + b and x2 + bx+c have a common factor (x - k) then k is​

Answer 1

Answer:

Given x+k is HCF of x

2

+ax+b and x

2

+cx+d

Therefore x+k is a factor of each expression.

Put x=−k is the given expressions.

(−k)

2

+(a)(−k)+b=0

⇒k

2

−ka+b=0 ………(1)

also (−k)

2

+c(−k)+d=0

⇒k

2

−ck+d=0 …..(2)

substract equation (2) from (1)

c.k−a.k−d+b=0

k(c−a)=d−b

⇒k=

c−a

d−b

.