Advertisements
Advertisements
प्रश्न
The expression 2x3 + ax2 + bx – 2 leaves remainder 7 and 0 when divided by 2x – 3 and x + 2 respectively. Calculate the values of a and b.
Advertisements
उत्तर
Let f(x) = 2x3 + ax2 + bx – 2
2x – 3 = 0 `\implies x = 3/2`
On dividing f(x) by 2x – 3, it leaves a remainder 7.
∴ `2(3/2)^3 + a(3/2)^2 + b(3/2) - 2 = 7`
`27/4 + (9a)/4 + (3b)/2 = 9`
`(27 + 9a+ 6b)/4 = 9`
27 + 9a + 6b = 36
9a + 6b – 9 = 0
3a + 2b – 3 = 0 ...(1)
x + 2 = 0 `\implies` x = –2
On dividing f(x) by x + 2, it leaves a remainder 0.
∴ 2(–2)3 + a(–2)2 + b(–2) – 2 = 0
–16 + 4a – 2b – 2 = 0
4a – 2b – 18 = 0 ...(2)
Adding (1) and (2), we get,
7a – 21 = 0
a = 3
Subsituting the value of a in (1), we get,
3(3) + 2b – 3 = 0
9 + 2b – 3 = 0
2b = –6
b = –3
APPEARS IN
संबंधित प्रश्न
Find the remainder when x3 + 3x2 + 3x + 1 is divided by 5 + 2x.
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(2x3 − 2x2 + ax − a) ; (x − a)
Find without division, the remainder in the following:
5x2 - 9x + 4 is divided by (x - 2)
What number should be added to 2x3 - 3x2 + 7x -8 so that the resulting polynomial is exactly divisible by (x-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 (without divisions) on dividing f(x) by x – 2, where f(x) = 5x2 – 1x + 4
Find the remainder (without division) on dividing 3x2 + 5x – 9 by (3x + 2)
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
If x25 + x24 is divided by (x + 1), the result is ______.
