Question

Find the values of k for which the quadratic equation 9x² - 3kx + k = 0 has equal roots.

Answer 1

Solution:
Given: Quadratic equation  9x²-3kx + k = 0 has equal roots
Let β be the equal roots of the equation

Thus 2β =(3k)/9=k/3 (Sum of the roots is equal to –b/a)

We get β=k/6 or β²⁼k²/36

Also that β²=k/9 (Product of the roots is equal to c/a)

k²/36=k/9

For k ≠ 0,k/36=1/9

thus k=4