Advertisements
Advertisements
प्रश्न
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).
उत्तर
Given f(x ) = (x -1 )(x - 2)+(-2x + 5)
= (x2 - 3x + 2) + (-2x + 5)
f(x) = x2 - 5x + 7
Substituting = 1
f(x) = 1 - 5 + 7 =3
when f(x) is divided by (x -1) , remainder = 3
substituting x = 2
f(x) = 4 - 10 + 7 = 1
when f(x) is divided by (x - 2), remainder = 1
`("x"^2 - 5"x" + 7)/("x"^2 - 3"x" + 2) = 1 (-2"x" + 5)/(("x" - 1)("x" - 2))`
and
when f(x) is divided by (x - 1)(x - 2), remainder = (-2x + 5).
APPEARS IN
संबंधित प्रश्न
Find the remainder when x3 – ax2 + 6x – a is divided by x – a.
Find the remainder when x4 – 3x2 + 2x + 1 is divided by x – 1.
Find the remainder when x4 + 1 is divided by x + 1.
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 2
If x3 + ax2 + bx + 6 has x – 2 as a factor and leaves a remainder 3 when divided by x – 3, find the values of a and b.
Find the value of ‘m’, if mx3 + 2x2 – 3 and x2 – mx + 4 leave the same remainder when each is divided by x – 2.
Find without division, the remainder in the following:
2x3 - 3x2 + 6x - 4 is divisible by (2x-3)
What number should be subtracted from x2 + x + 1 so that the resulting polynomial is exactly divisible by (x-2) ?
Find the remainder (without divisions) on dividing f(x) by x – 2, where f(x) = 2x3 – 7x2 + 3
Find the remainder (without division) when 2x3 – 3x2 + 7x – 8 is divided by x – 1 (2000)
