Advertisements
Advertisements
प्रश्न
Using the remainder theorem, find the remainders obtained when x3 + (kx + 8 )x + k is divided by x + 1 and x − 2.
Hence, find k if the sum of the two remainders is 1.
Advertisements
उत्तर
Remainder theorem :
Dividend = Divisors × Quotient + Remainder
∴ Let f(x) = x3 + (kx + 8 )x + k
= x3 + kx2 + 8x + k
Dividing f(x) by x + 1 gives remainder as R1
∴ f (−1) = R1
Also, f(2) = R2
∴ f (−1) = (−1)3 + k(−1)2 + 8(−1) + k
= −1 + k − 8 + k
= 2k − 9 = R1
f(2) = (2)3 + k (2)2 + 8(2) + k
= 8 + 4k + 16 + k
= 5k + 24 = R2
Also,Sum of remainders = R1 + R2 = 1
∴ (2k − 9) + (5k +24) = 1
7k + 15 = 1
7k = −14
k = −2
APPEARS IN
संबंधित प्रश्न
What must be subtracted from 16x3 – 8x2 + 4x + 7 so that the resulting expression has 2x + 1 as a factor?
What number should be added to 3x3 – 5x2 + 6x so that when resulting polynomial is divided by x – 3, the remainder is 8?
Using remainder theorem, find the value of m if the polynomial f(x)= x3 + 5x2 -mx +6 leaves a remainder 2m when divided by (x-1),
What number should be added to polynomial f(x)= 12x3 + 16x2 - 5x - 8 so that the resulting polynomial is exactly divisible by (2x - 1) ?
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.
Find the value of p if the division of px3 + 9x2 + 4x - 10 by (x + 3) leaves the remainder 5.
When divided by x – 3 the polynomials x3 – px2 + x + 6 and 2x3 – x2 – (p + 3)x – 6 leave the same remainder. Find the value of ‘p’.
Find the remainder when 2x3 – 3x2 + 4x + 7 is divided by x – 2
By remainder theorem, find the remainder when, p(x) is divided by g(x) where, p(x) = x3 – 2x2 – 4x – 1; g(x) = x + 1
Check whether p(x) is a multiple of g(x) or not:
p(x) = 2x3 – 11x2 – 4x + 5, g(x) = 2x + 1
