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Zeroes of a Polynomial

When x 2 -2...

Question

When $x^{2} - 2 x + k$ divided the polynomial $x^{2} - {6 x}^{3} + 16 x^{2} - 25 x + 10$ the reminder is (x+a), the value of is

-5

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-3

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Solution

The correct option is A -5
We have,

Given the reminder $x + a$

Then,

By above image

Reminder is

$(4 k - 25 + 16 - 2 k) x + 10 [- k (8 - k)] = x + a$

According to given question,

$(2 k - 9) x + [10 - 8 k + k^{2}] = x + a$

On comparing both side and we get,

$2 k - 9 = 1$

$\Rightarrow 2 k = 10$

$\Rightarrow k = 5$

Also,

$10 - 8 k + k^{2} = a$

$\Rightarrow 10 - 8 (5) + 5^{2} = a$

$\Rightarrow 10 - 40 + 25 = a$

$\Rightarrow a = - 5$
Hence, this is the answer.

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