Question:
Very-Short-Answer Questions
Find the values of $k$ for which the quadratic equation $9 x^{2}-3 k x+k=0$ has equal roots.
Solution:
It is given that the quadratic equation $9 x^{2}-3 k x+k=0$ has equal roots.
$\therefore D=0$
$\Rightarrow(-3 k)^{2}-4 \times 9 \times k=0$
$\Rightarrow 9 k^{2}-36 k=0$
$\Rightarrow 9 k(k-4)=0$
$\Rightarrow k=0$ or $k-4=0$
$\Rightarrow k=0$ or $k=4$
Hence, 0 and 4 are the required values of k.
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