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: 2x² + kx + 3 = 0

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

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

Given quadratic equation: 2x² + kx + 3 = 0

By comparing these two equations, we get:

a = 2, b = k and c = 3

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:

$(k)^2 - 4 (2) (3) = 0$

$\therefore k^2 - 24 = 0$

$\therefore k^2 = 24$

$\therefore k^2 = (2 \sqrt {6})^2$

Therefore, $k = 2\sqrt {6}$ and $k = - 2\sqrt {6}$

Please do press “Heart” button if you liked the solution.

Contact us