Question

2x4-ax3+4x2-x+2 divisible by 2x+1 find the value of a

Answer 1

Hope this will be helping you.

Answer 2

Given:

2x4 - ax3 + 4x2 - x + 2 divisible by 2x + 1.

To find:

The value of a.

Solution:

As given,

we have a polynomial p(x):

$2 {x}^{4} - a {x}^{3} + 4 {x}^{2} - x + 2$

which is divisible by 2x + 1.

This means,

If 2x + 1 = 0

x = -1/2,

Then

p(-1/2) = 0

So,

On putting x = -1/2 in the given polynomial, we get

$2 { (\frac{ - 1}{2} )}^{4} - a { (\frac{ - 1}{2} )}^{3} + 4 { (\frac{ - 1}{2} )}^{2} - ( \frac{ - 1}{2}) + 2 = 0$

On solving the above, we get

$2 (\frac{1}{16} ) - a( \frac{ - 1}{8}) + 4( \frac{1}{4} ) + \frac{1}{2} + 2 = 0$

$\frac{1}{8} + \frac{a}{8} + 1 + \frac{1}{2} + 2 = 0$

On multiplying both sides by 8, we get

${1 + a + 8 + 4 + 16} = 0$

Adding all the terms, we get

$a + 29 = 0$

$a = - 29$

Hence, the value of a is -29.