What is the <strong>GREATEST</strong> value of k for which 2x^{2}-4x+k=0 has real roots?

Explanation

For real roots, the discriminant D \geq 0. Thus, (-4)^2 - 4(2)(k) \geq 0 \implies 16 - 8k \geq 0 \implies k \leq 2. The greatest value is 2.

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