Advertisements
Advertisements
Question
The polynomials 2x3 – 7x2 + ax – 6 and x3 – 8x2 + (2a + 1)x – 16 leaves the same remainder when divided by x – 2. Find the value of ‘a’.
Advertisements
Solution
Let f(x) = 2x3 – 7x2 + ax – 6
x – 2 = 0 `\implies` x = 2
When f(x) is divided by (x – 2), remainder = f(2)
∴ f(2) = 2(2)3 – 7(2)2 + a(2) – 6
= 16 – 28 + 2a – 6
= 2a – 18
Let g(x) = x3 – 8x2 + (2a + 1)x – 16
When g(x) is divided by (x – 2), remainder = g(2)
∴ g(2) = (2)3 – 8(2)2 + (2a + 1)(2) – 16
= 8 – 32 + 4a + 2 – 16
= 4a – 38
By the given condition, we have:
f(2) = g(2)
2a – 18 = 4a – 38
4a – 2a = 38 – 18
2a = 20
a = 10
Thus, the value of a is 10.
APPEARS IN
RELATED QUESTIONS
When x3 + 3x2 – mx + 4 is divided by x – 2, the remainder is m + 3. Find the value of m.
Find the number which should be added to x2 + x + 3 so that the resulting polynomial is completely divisible by (x + 3).
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 x2 + x + 1 so that the resulting polynomial is exactly divisible by (x-2) ?
What number should be added to 2x3 - 3x2 + 7x -8 so that the resulting polynomial is exactly divisible by (x-1) ?
If on dividing 2x3 + 6x2 – (2k – 7)x + 5 by x + 3, the remainder is k – 1 then the value of k is
When 2x3 – 9x2 + 10x – p is divided by (x + 1), the remainder is – 24.Find the value of p.
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
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
