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Mathematics

Find the value of k for which the equation 3x2 - 6x + k = 0 has distinct and real roots.

Quadratic Equations

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Answer

Comparing 3x2 - 6x + k = 0 with ax2 + bx + c = 0 we get,

a = 3, b = -6 and c = k.

Since equations have distinct and real roots,

∴ D > 0

⇒ (-6)2 - 4.(3).(k) > 0

⇒ 36 - 12k > 0

⇒ 12k < 36

⇒ k < 3.

Hence, k < 3.

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