Question

determine the value of b for which the polynomial 5x^3 - x^2 + 4x+b is divided by 2x-1

Answer 1

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Answer 2

Hi friend, Harish here.

Here is your answer:

Given that,

1) An expression 5x³ - x² + 4x + b

2) 2x - 1 is a factor of Above expression.

To  find, 

The value of b.

Solution,

It is given that, 2x - 1 is a factor.

So, When we take (2 x - 1)  = 0 , Then The polynomial is also zero.

So, If 2x - 1 =0, Then,

$x= \frac{1}{2}$

So, Substitute x value in the polynomial.

Then,

$5( \frac{1}{2})^{3} + (\frac{1}{2})^{2} + 4( \frac{1}{2}) +b = 0$

⇒ $\frac{5}{8}+ \frac{1}{4}+ \frac{4}{2}+b =0$

⇒ $\frac{5+2+16}{8} +b = 0$

⇒ $b = - ( \frac{23}{8})$

Therefore the value of b is -23/8.
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Hope my answer is helpful to you.