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