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प्रश्न
Find the nonzero value of k for which the roots of the quadratic equation `9x^2-3kx+k=0` are real and equal.
उत्तर
The given equation is `9x^2-3kx+k=0`
This is of the form `ax^2+bx+c=0,` where `a=9, b=-3k and c=k`
∴ `D=b^2-4ac=(-3k)^2-4xx9xxk=9k^2-36k`
The given equation will have real and equal roots if D = 0.
∴` 9k^2-36k=0`
⇒` 9k(k-4)=0`
⇒ `k=0 or k-4=0`
⇒`k=0 or k=4`
But, k ≠ 0 (Given)
Hence, the required values of k is 4.
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