Question

38. If $2 x+3$ is a factor of the cubic polynomial $p(x)=2 x^{3}+9 x^{2}-a x-b$ and $a+b=16$, then find the values of $a$ and $b$.​

Answer 1

Answer:

Let g(x)=2x−3

Zero of g(x)⇒2x−3=0⇒

x=3/2

∴f(3/2)=2(3/2)

3

−9(3/2)

2

+

2

3

+k.

=

2

27

−

4

81

−

2

3

+k.

∴(2x−3) is a factor of f(x)

∴ f(x)=0 ⇒ f(3/2)=0

or,

4

27

−

4

81

+

2

3

+k=0.

or,

4

−54

+

2

3

+k=0.

or,

4

−54+6

+k=0.

or, k=

4

48

⇒

k=12