Compute maximum value of k that will make the discriminant of the quadratic equation positive : $x^{2} - 6 x + k = 0$ .

4

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8

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12

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Solution

The correct option is A $8$
The given quadratic equation is : $x^{2} - 6 x + k = 0$ .
In this equation, $a = 1, b = - 6, c = k$ .
The value of the discriminant, $D = 6^{2} - 4 \times 1 \times k$
Now, $D > 0 ⟹ 36 - 4 k > 0$
$k < 9$
If $k < 9$ , the highest integer value that k can take is $8.$

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