Find the value of $k$ for which the equation $x^{2} - 6 x + k = 0$ has distinct roots.

k > 9

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k = 6, 7

only

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k < 9

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k = 9

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Solution

The correct option is B $k < 9$
$x^{2} - 6 x + k = 0$ has
discreminant $D = b^{2} - 4 a c$
$= 36 - 4 k$
For real roots $D > 0$ $\Rightarrow$ $36 - 4 k > 0$
$\Rightarrow$ $k < 9$

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