Advertisements
Advertisements
प्रश्न
Find the value of a, if the division of ax3 + 9x2 + 4x – 10 by x + 3 leaves a remainder 5.
Advertisements
उत्तर
Let f(x) = ax3 + 9x2 + 4x – 10
x + 3 = 0
`\implies` x = –3
On dividing f(x) by x + 3, it leaves a remainder 5.
∴ f(–3) = 5
a(–3)3 + 9(–3)2 + 4(–3) – 10 = 5
–27a + 81 – 12 – 10 = 5
-27a + 81 - 22 = 5
-27a + 59 = 5
-27a = 5 - 59
-27a = -54
a = `(-54)/-27`
a = 2
APPEARS IN
संबंधित प्रश्न
Check whether 7 + 3x is a factor of 3x3 + 7x.
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 + 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.
What number should be subtracted from x3 + 3x2 – 8x + 14 so that on dividing it by x – 2, the remainder is 10?
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(54m3 + 18m2 − 27m + 5) ; (m − 3)
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).
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x - 4
Find the remainder (without division) on dividing f(x) by (2x + 1) where f(x) = 4x2 + 5x + 3
(x – 2) is a factor of the expression x3 + ax2 + bx + 6. When this expression is divided by (x – 3), it leaves the remainder 3. Find the values of a and b.
