Home
Class 12
MATHS
When polynomial f(x) is divided (x- 1) a...

When polynomial f(x) is divided `(x- 1)` and `(x -2)` it leaves remainder 5 and 7 respectively. What is the remainder when f(x) is divided by `(x-1)(x-2)`?

Text Solution

Verified by Experts

The correct Answer is:
`rArr a=-1, b=3`
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATION & EXPRESSION

    FIITJEE|Exercise SOLVED PROBLEMS (SUBJECTIVE)|12 Videos
  • QUADRATIC EQUATION & EXPRESSION

    FIITJEE|Exercise SOLVED PROBLEMS (OBJECTIVE)|27 Videos
  • PROGRESSION & SERIES

    FIITJEE|Exercise NUMERICAL BASED|3 Videos
  • SET, RELATION & FUNCTION

    FIITJEE|Exercise Exercise 3|8 Videos

Similar Questions

Explore conceptually related problems

If a polynomial f (x) is divided by (x - 3) and (x - 4) it leaves remainders as 7 and 12 respectively, then find the remainder when f (x) is divided by (x-3)(x-4) .

A polynomial f(x) when divided by (x-5)and (x-7) leaves remainders 6 and 16 , respectively. Find the remainder when f(x) is divided by (x-5)(x-7) .

When a polynomial f(x) is divisible by x-3 and x+6, the respective remainders are 7 and 22. What is the remainder when f(x) is divided by (x-3)(x+6) ?

If f(x) = x^4 - 2 x^3 + 3 x^2 - ax +b a polynomial such that when it is divided by (x-1) and (x+1); the remainders are 5 and 19 respectively. Determine the remainder when f(x) is divided by (x-2).

Consider an unknow polynomial which divided by (x - 3) and (x-4) leaves remainder 2 and 1, respectively. Let R(x) be the remainder when this polynomial is divided by (x-3)(x-4) . If equations R(x) = x^(2)+ ax +1 has two distint real roots, then exhaustive values of a are.

If f(x)=x^(4)-2x^(3)+3x^(2)-ax+b is a polynomial such that when1it is divided by x-1 and x+1, remainders are 5 and 19 respectively.Determine the remainder when f(x) is divided by x-1.

Given f(x) is a cubic polynomial in x . If f(x) is divided by (x+3),(x+4),(x+5)and (x+6) , then it leaves the remainders 0, 0 , 4 and 6 respectively . Find the remainder when f(x) is divided by x+7 .

Given f(x) is a cubic polynomial in x .If f(x) is divided by (x+3),(x+4),(x+5) and (x+6), then it leaves the remainders 0,0,4 and 6 respectively.Find the remainder when f(x) is dividedby x+7.

If f(x)=x^(4)-2x^(3)+3x^(2)-ax+b is a polynomial such that when it is divided by x-1 and x+1 the remainders are respectively 5 and 19.Determine the remainder when f(x) is divided by x-2 .