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

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

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Solution

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

Concept: Nature of Roots
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