Question

if one root of the equation 3xpower2+Kx+81=0 is the squar of the other then find k​

Answer 1

Step-by-step explanation:

3x

2

+kx−81=0

Here, a=3,b=k,c=−81

Let α,β be the roots of the equation.

From the given question,

⇒ β=α

2

⇒ α.β=

a

c

⇒ α.α

2

=

3

−81

⇒ α

3

=−27

⇒ α=−3

⇒ 3(−3)

2

+k(−3)−81=0

⇒ 3(9)−3k−81=0

⇒ 27−3k−81=0

⇒ 3k=−54

∴ k=−18