Question

find the value of 'a', if
$2 {x}^{4} - ax + 4 {x}^{2} - x + 2$
Is divisible by
$2x + 1$

Answer 1

$2x + 1 = 0 \\ x = \frac{ - 1}{2} \\ put \: this \: value \: in \: polynomial \\ 2 {x}^{4} - a {x}^{3} + 4 {x}^{2} - x + 2 \\ 2( { \frac{ - 1}{2} )}^{4} - a( { \frac{ - 1}{2} )}^{3} + 4 ({ \frac{ - 1}{2} })^{2} - \frac{ - 1}{2} + 2 = 0 \\ \frac{1}{8} + \frac{a}{8} + 1 + \frac{1}{2} + 2 = 0 \\ \frac{1}{8} + \frac{a}{8} + \frac{1}{2} + 3 = 0 \\ \\ \frac{1 + a + 4 + 24}{8} = 0 \\ a + 2 9= 0 \\ a = - 29$

Answer 2

Answer:

2x+1=0

x=

2

−1

putthisvalueinpolynomial

2x

4

−ax

3

+4x

2

−x+2

2(

2

−1

)

4

−a(

2

−1

)

3

+4(

2

−1

)

2

−

2

−1

+2=0

8

1

+

8

a

+1+

2

1

+2=0

8

1

+

8

a

+

2

1

+3=0

8

1+a+4+24

=0

a+29=0

a=−29