please solve 13 number
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ANSWER:
Given:
- When, p(x) = x^3 - 6x^2 + 2x - k, is divided by (1 - 2x), Remainder = R1
- When, g(x) = kx^3 + 12x^2 + 14x - 3, is divided by (2x + 1), Remainder = R2
- R1 - R2 = 25/8
To Find:
- Value of k
Solution:
We are given that,
And,
Taking p(x) first,
We have,
That is,
Let, 1 - 2x = 0.
So, x = 1/2
As,
So, by Factor Theorem,
So,
So,
Taking LCM,
So,
Taking g(x) now,
We have,
That is,
Let, 2x + 1 = 0.
So, x = -1/2
As,
So, by Factor Theorem,
So,
So,
Taking LCM,
So,
Now, we are also given that,
From (1) & (2),
Combining fractions,
So,
Hence,
Therefore, the value of k is 4.
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