Question

the quadratic equation x, which when divided by (x-A),(x-B,(x-C) leaves a remainder of 11,22,37 is ? plzz reply fast. it is urgent

Answer 1

Using Remiander theorem

f(a) is the remainder when f(x) is divided by x-a

when f(x) is divided by q(x) the remainder will be having degree less than q(x) so when P(x) is divided by (x-a),(x-b),(x-c) the remainders are P(a),P(b) and P(c) respectively

therefore P(x)=(x-a)(x-b)(x-c)g(x) + (px^2+qx+r) where (px^2+qx+r)is remainder g(x) is the quotient

P(a)=pa^2+qa+r=a --- (I)

P(b)=pb^2+qb+r=b----(II)

P(c)=pc^2+qc+r=c-----(III)

Closely observing u can q=1 p and r =0

So remiander will be x

and Secondly you could have also solved equations by using II-I and III-I.

Answer 2

Answer:

The above explanation is exactly correct.