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Q.

For what value of ‘k’ does the quadratic equation kx (x – 2) + 6 = 0 have two equal roots?


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a

k = 7

b

k = 8

c

k = 6

d

k = 2 

answer is C.

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Detailed Solution

Given equation is kx (x – 2) + 6 = 0.
We know that the standard form of a quadratic equation is a x 2 +bx+c=0,a≠0  , for which the roots are x= −b± b 2 −4ac 2a  .
Let us expand the given equation.
⇒k x 2 −2kx+6=0  
On comparing the above obtained equation with general form, we get,
a = k, b = -2k and c = 6.
Now it is given that the equation has two equal roots so,
Discriminant = 0 ⇒D= b 2 −4ac=0  
⇒ (−2k) 2 −4(6)k=0 ⇒4 k 2 −24k=0  
⇒4k(k−6)=0  
Either 4k=0 or k−6=0  
⇒k=0 or k=6  
But here k≠0  , because the coefficient of x 2   in the equation k x 2 −2kx+6=0   should not be 0.
So, the value of k for the quadratic equation k x 2 −2kx+6=0   is k=6.
Therefore, the correct option is 3.
 
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