Advertisements
Advertisements
प्रश्न
If on dividing 2x3 + 6x2 – (2k – 7)x + 5 by x + 3, the remainder is k – 1 then the value of k is
विकल्प
2
– 2
– 3
3
Advertisements
उत्तर
f(x) = 2x3 + 6x2 – (2k – 7)x + 5
g(x) = x + 3
Remainder = k – 1
If x + 3 = 0,
then x = –3
∴ Remainder will be
f(–3) = 2(–3)2 + 6(–3)2 – (2k – 7)(–3) + 5
= –54 + 54 + 3(2k – 7) + 5
= –54 + 54 + 6k – 21 + 5
= 6k – 16
∴ 6k – 16 = k – 1
6k – k = –1 + 16
⇒ 5k – 15
k = `(15)/(5)` = 3
∴ k = 3.
APPEARS IN
संबंधित प्रश्न
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x + π.
Find the remainder when x4 + 1 is divided by x + 1.
use the rernainder theorem to find the factors of ( a-b )3 + (b-c )3 + ( c-a)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).
The polynomial f(x) = ax4 + x3 + bx2 - 4x + c has (x + 1), (x-2) and (2x - 1) as its factors. Find the values of a,b,c, and remaining factor.
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x + 2
Using remainder theorem, find the remainder on dividing f(x) by (x + 3) where f(x) = 3x3 + 7x2 – 5x + 1
By remainder theorem, find the remainder when, p(x) is divided by g(x) where, p(x) = 4x3 – 12x2 + 14x – 3; g(x) = 2x – 1
By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial: x4 + 1; x – 1
A polynomial in ‘x’ is divided by (x – a) and for (x – a) to be a factor of this polynomial, the remainder should be ______.
