Advertisements
Advertisements
प्रश्न
When x3 + 2x2 – kx + 4 is divided by x – 2, the remainder is k. Find the value of constant k.
Advertisements
उत्तर
Let f(x) = x3 + 2x2 – kx + 4
x – 2 = 0 `\implies` x = 2
On dividing f(x) by x – 2, it leaves a remainder k.
∴ f(2) = k
(2)3 + 2(2)2 – k(2) + 4 = k
8 + 8 – 2k + 4 = k
20 = 3k
`k = 20/3 = 6(2)/3`
APPEARS IN
संबंधित प्रश्न
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x + π.
What must be subtracted from 16x3 – 8x2 + 4x + 7 so that the resulting expression has 2x + 1 as a factor?
Using the Remainder and Factor Theorem, factorise the following polynomial:
`x^3 + 10x^2 - 37x + 26`
Find the values of a and b when the polynomials f(x)= 2x2 -5x +a and g(x)= 2x2 + 5x +b both have a factor (2x+1).
A polynomial f(x) when divided by (x - 1) leaves a remainder 3 and when divided by (x - 2) leaves a remainder of 1. Show that when its divided by (x - i)(x - 2), the remainder is (-2x + 5).
Find the remainder when the polynomial f(x) = 2x4 - 6x3 + 2x2 - x + 2 is divided by x + 2.
Using remainder theorem, find the remainder on dividing f(x) by (x + 3) where f(x) = 2x2 – 5x + 1
Using remainder theorem, find the remainder on dividing f(x) by (x + 3) where f(x) = 3x3 + 7x2 – 5x + 1
Determine which of the following polynomials has x – 2 a factor:
4x2 + x – 2
The remainder, when x3 – x2 + x – 1 is divided by x + 1, is ______.
