Question

kx(x-2)+6=0 The roots of each of the quadratic equation are real and equal, find k.

Answer 1

kx(x - 2) + 6 = 0 


kx^2 - 2kx + 6 = 0 


kx^2 - 2kx + 6 = 0 




Discriminant = b^2 - 4ac
                       = (-2k)^2 - 4(6)(k)
                       = 4k^2 - 24k



We know,for equal roots,discriminant = 0 


Hence, 4k^2 - 24k = 0
             4k(k - 6) = 0 
             

4k = 0         Or    k - 6=  0 

k = 0/4 = 0     Or   k = 6 






k = 6 Or 0

Answer 2

Hey!

Here is your answer!
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QUADRATIC EQUATION :

kx(x-2)+6=0

kx²-2kx+6=0

On comparing with,

ax²+bx+c=0

We get,

a=k, b= -2k and c=6
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We know that, for real and equal roots

Discriminant (D) =0

b²-4ac=0

(-2k)² - 4×k×6=0

4k²- 24k=0

4k(k-6)=0

So, k=0 or k=6
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Hope it's satisfactory!