**Q. ****Find the values of k for following quadratic equation, so that it has equal roots: kx (x -2) + 6 = 0**

**Ans: **

Given quadratic equation: kx (x – 2) + 6 = 0

by simplifying this we get kx^{2} – 2 kx + 6 = 0

Let’s compare the given equation with standard quadratic equation:

Standard quadratic equation: a x^{2} + bx + c = 0

Given quadratic equation: kx^{2} – 2 k x + 6 = 0

By comparing these two equations, we get:

a = k, b = – 2 k and c = 6

Next, we now that if a quadratic equation has two equal roots, its discriminant is 0,

Let’s substitute values of a, b and C from above, we get:

We get 2 values of k i.e. k = 0 and k = 6.

We reject k = 0 (∵ equation k x^{2} – 2 k x + 6 = 0 becomes zero at k = 0)

**therefore k = 6. **

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