Find the values of k for which the quadratic equation 9x^{2} - 3kx + k = 0 has equal roots.

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#### Solution

Solution:

Given: Quadratic equation 9x^{2}-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 β^{2=}k^{2}/36

Also that β^{2}=k/9 (Product of the roots is equal to c/a)

k^{2}/36=k/9

For k ≠ 0,k/36=1/9

thus k=4

Concept: Nature of Roots

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