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. Find the values of k for each of the following quadratic equations, so that they have two equal roots. kx(x - 2) + 6 = 0

. Find the values of k for each of the following quadratic equations, so that they have two equal roots. 
 kx(x - 2) + 6 = 0

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5965 Points
one year ago
Dear Student

kx(x- 2) + 6 = 0
orkx^2- 2kx+ 6 = 0
On Comparing the given equation withax^2+bx+c= 0,
a=k,b= - 2kandc= 6

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

For equal roots, we know,b^2-4ac=0
4k^2-24k=0
4k(k- 6) = 0

Either 4k= 0 ork= 6 = 0
k= 0 ork= 6
However, ifk= 0,
then the equation will not have the terms 'x^2' and 'x'.
Therefore, if this equation has two equal roots,kshould be 6 only.

Thanks

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