Advertisements
Advertisements
प्रश्न
When x3 + 2x2 – kx + 4 is divided by x – 2, the remainder is k. Find the value of constant k.
Advertisements
उत्तर
Let f(x) = x3 + 2x2 – kx + 4
x – 2 = 0 `\implies` x = 2
On dividing f(x) by x – 2, it leaves a remainder k.
∴ f(2) = k
(2)3 + 2(2)2 – k(2) + 4 = k
8 + 8 – 2k + 4 = k
20 = 3k
`k = 20/3 = 6(2)/3`
संबंधित प्रश्न
Find the remainder when x3 + 3x2 + 3x + 1 is divided by `x - 1/2`
Check whether 7 + 3x is a factor of 3x3 + 7x.
Find 'a' if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
Using the Remainder and Factor Theorem, factorise the following polynomial:
`x^3 + 10x^2 - 37x + 26`
Using the Remainder Theorem, factorise the expression 3x3 + 10x2 + x – 6. Hence, solve the equation 3x3 + 10x2 + x – 6 = 0
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(2x3 − 2x2 + ax − a) ; (x − a)
Find the values of m and n when the polynomial f(x)= x3 - 2x2 + m x +n has a factor (x+2) and leaves a remainder 9 when divided by (x+1).
What number should be subtracted from the polynomial f(x)= 2x3 - 5x2 +8x -17 so that the resulting polynomial is exactly divisible by (2x - 5)?
If x + 1 is a factor of 3x3 + kx2 + 7x + 4, then the value of k is
If x25 + x24 is divided by (x + 1), the result is ______.
