Find the values of k for following quadratic equation

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 kx² – 2 kx + 6 = 0

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

Standard quadratic equation: a x² + bx + c = 0

Given quadratic equation: kx² – 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,

$\therefore b^2 - 4 a c = 0$

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

$(- 2 k)^2 - 4 (k) (6) = 0$

$\therefore 4 k^2 - 24 k = 0$

$\therefore 4 k (k - 6) = 0$

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

We reject k = 0 (∵ equation k x² – 2 k x + 6 = 0 becomes zero at k = 0)

therefore k = 6.

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