Advertisements
Advertisements
प्रश्न
Find the value of ‘m’, if mx3 + 2x2 – 3 and x2 – mx + 4 leave the same remainder when each is divided by x – 2.
Advertisements
उत्तर
Let f(x) = mx3 + 2x2 – 3
g(x) = x2 – mx + 4
It is given that f(x) and g(x) leave the same remainder when divided by (x – 2).
Therefore, we have:
f(2) = g(2)
m(2)3 + 2(2)2 – 3 = (2)2 – m(2) + 4
8m + 8 – 3 = 4 – 2m + 4
10m = 3
m = `3/10 `
APPEARS IN
संबंधित प्रश्न
Use the Remainder Theorem to factorise the following expression:]
`2x^3 + x^2 - 13x + 6`
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 1
Find without division, the remainder in the following:
2x3 - 3x2 + 6x - 4 is divisible by (2x-3)
Find the values of a and b when the factors of the polynomial f(x)= ax3 + bx2 + x a are (x+3) and (2x-1). Factorize the polynomial completely.
When x3 + 3x2 – kx + 4 is divided by (x – 2), the remainder is k. Find the value of k.
Find ‘a’ if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
When a polynomial f(x) is divided by (x – 1), the remainder is 5 and when it is,, divided by (x – 2), the remainder is 7. Find – the remainder when it is divided by (x – 1) (x – 2).
Determine which of the following polynomials has x – 2 a factor:
4x2 + x – 2
Without actual division, prove that 2x4 – 5x3 + 2x2 – x + 2 is divisible by x2 – 3x + 2. [Hint: Factorise x2 – 3x + 2]
4x2 – kx + 5 leaves a remainder 2 when divided by x – 1. The value of k is ______.
