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Question
Find the value of k for which the equation 3x2 – 6x + k = 0 has distinct and real roots.
Solution
3x2 – 6x + k = 0
Here, a = 3, b = – 6 and c = k
Since the roots are distinct and real,
b2 – 4ac > 0
⇒ (– 6)2 – 4 × 3 × k > 0
⇒ 36 – 12k > 0
⇒ 36 > 12k
⇒ 3 > k
⇒ k < 3
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