Question

find the value of 'k' so that the quadratic equation kx(5x-6)+9=0 has two equal roots​

Answer 1

Answer:

Quadratic equation has equal roots then b

2

−4ac=0

Given that kx

2

−2kx+6=0

Here a=k,b=−2k and c=6

Now, (−2k)

2

−4×k×6=0

⇒4k

2

−24k=0

⇒4k(k−6)=0

⇒k=0 or k=6

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Answer 2

Given,

The equation: kx(5x-6)+9=0.

The equation has two equal roots.

To Find,

The value of actual 'k'.

Solution,

We know if the quadratic equation, a$x^{2}$+bx+c=o, has equal roots then $b^{2}$-4ac=0.

Given an equation,

kx(5x-6)+9=0.

⇒5$kx^{2}$-6kx+9=0.

Here a=5k,b=−6k, and c=9.

So here the D =  $b^{2}$-4ac=36$k^{2}$-4×5k×9.

D=0.

⇒36k-4×5k×9=0.

⇒36$k^{2}$-180k=0.

⇒36k×(k-5)=0.

⇒Either k=0(Which is not possible as this is a quadratic equation)

⇒0r, k=5.

Hence , The  value of 'k' = 5.