Advertisements
Advertisements
Question
4x2 – kx + 5 leaves a remainder 2 when divided by x – 1. The value of k is ______.
Options
– 6
6
7
– 7
Solution
4x2 – kx + 5 leaves a remainder 2 when divided by x – 1. The value of k is 7.
Explanation:
Let f(x) = 4x2 – kx + 5
When f(x) is divided by x – a then remainder = f(a)
Given f(x) is divided by x – 1 leaves a remainder 2
∴ f(1) = 2
`\implies` 4 × 12 – k + 5 = 2
`\implies` 4 – k + 5 = 2
`\implies` 9 – k = 2
`\implies` k = 9 – 2 = 7
RELATED QUESTIONS
Using remainder theorem, find the value of k if on dividing 2x3 + 3x2 – kx + 5 by x – 2, leaves a remainder 7.
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
2x – 1
What number should be added to 3x3 – 5x2 + 6x so that when resulting polynomial is divided by x – 3, the remainder is 8?
What number should be subtracted from x3 + 3x2 – 8x + 14 so that on dividing it by x – 2, the remainder is 10?
Polynomials bx2 + x + 5 and bx3 − 2x + 5 are divided by polynomial x - 3 and the remainders are m and n respectively. If m − n = 0 then find the value of b.
Find without division, the remainder in the following :
x3 + 8x2 + 7x- 11 is divisible by (x+4)
Find the remainder (without division) on dividing f(x) by (2x + 1) where f(x) = 4x2 + 5x + 3
If x51 + 51 is divided by x + 1, then the remainder is
By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x3 – 6x2 + 2x – 4, g(x) = `1 - 3/2 x`
Check whether p(x) is a multiple of g(x) or not:
p(x) = x3 – 5x2 + 4x – 3, g(x) = x – 2
