Advertisements
Advertisements
प्रश्न
If x + 1 is a factor of 3x3 + kx2 + 7x + 4, then the value of k is
विकल्प
– 1
0
6
10
Advertisements
उत्तर
f(x) = 3x3 + kx2 + 7x + 4
g(x) = x + 1
Remainder = 0
Let x + 1 = 0,
then x = – 1
f(– 1) = 3(– 1)3 + k(– 1)2 + 7(– 1) + 4
= – 3 + k – 7 + 4
= k – 6
∴ Remainder = 0
∴ k – 6 = 0
⇒ k = 6.
APPEARS IN
संबंधित प्रश्न
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x.
Find the remainder when x3 – ax2 + 6x – a is divided by x – a.
The polynomials ax3 + 3x2 – 3 and 2x3 – 5x + a, when divided by x – 4, leave the same remainder in each case. Find the value of a.
Find the number which should be added to x2 + x + 3 so that the resulting polynomial is completely divisible by (x + 3).
Polynomials bx2 + x + 5 and bx3 − 2x + 5 are divided by polynomial x - 3 and the remainders are m and n respectively. If m − n = 0 then find the value of b.
Find the values of p and q in the polynomial f(x)= x3 - px2 + 14x -q, if it is exactly divisible by (x-1) and (x-2).
Find the value of p if the division of px3 + 9x2 + 4x - 10 by (x + 3) leaves the remainder 5.
Find the remainder (without division) on dividing f(x) by (2x + 1) where f(x) = 4x2 + 5x + 3
Find the remainder when 2x3 – 3x2 + 4x + 7 is divided by 2x + 1
Without actual division, prove that 2x4 – 5x3 + 2x2 – x + 2 is divisible by x2 – 3x + 2. [Hint: Factorise x2 – 3x + 2]
