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प्रश्न
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’.
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उत्तर
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.
संबंधित प्रश्न
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x+1.
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
2x – 1
What number should be subtracted from x3 + 3x2 – 8x + 14 so that on dividing it by x – 2, the remainder is 10?
What number should be subtracted from x2 + x + 1 so that the resulting polynomial is exactly divisible by (x-2) ?
Find the remainder (without divisions) on dividing f(x) by x – 2, where f(x) = 2x3 – 7x2 + 3
Find the remainder (without division) on dividing 3x2 + 5x – 9 by (3x + 2)
Find the remainder when 3x3 – 4x2 + 7x – 5 is divided by (x + 3)
If x3 + 6x2 + kx + 6 is exactly divisible by (x + 2), then k = ?
By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x3 – 3x2 + 4x + 50, g(x) = x – 3
Check whether p(x) is a multiple of g(x) or not:
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