Question

for what value of a is the polynomial 2x^3 - 9x^2 + x + a exactly divisible by 2x - 3 ?​

Answer 1

Step-by-step explanation:

$as \: the \: polynmial \: is \: divided \: by \: 2x - 3 \: \\ so \: x = \frac{3}{2} \\ now \: putting \: the \: value \: of \: x \: we \: get \: the \: value \: of \: a \\ 2 {x}^{3} - 9 {x}^{2} + x + a = 0 \\ 2 {( \frac{3}{2} )}^{3} - 9 {( \frac{3}{2} )}^{2} + \frac{3}{2} + a = 0 \\ 2 \times \frac{27}{8} - 9 \frac{9}{4} + \frac{3}{2} + a = 0 \\ \frac{27}{4} - \frac{81}{4} + \frac{3}{2} + a = 0 \\ \frac{27 - 81 + 6}{4} + a = 0 \\ - \frac{48}{4} + a = 0 \\ a = \frac{48}{4} = 12$

Answer 2

Answer:

asthepolynmialisdividedby2x−3

sox=

2

3

nowputtingthevalueofxwegetthevalueofa

2x

3

−9x

2

+x+a=0

2(

2

3

)

3

−9(

2

3

)

2

+

2

3

+a=0

2×

8

27

−9

4

9

+

2

3

+a=0

4

27

−

4

81

+

2

3

+a=0

4

27−81+6

+a=0

−

4

48

+a=0

a=

4

48

=12