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1. The discriminant of the given equation 6x² – 2x + k as required is; 4 – 24k.

   The value of k for which the equation will result in two different real solutions is; k < 1/6.

   What is the discriminant of the given quadratic function?

   Since the discriminant for the standard form quadratic equation; y = ax² + bx +c is given by the formula;

   Discriminant, D = b² – 4ac

   On this note, since; a = 6, b = -2 and c = k.

   Discriminant, D = (-2)² – (4 × 6 × k).

   D = 4 – 24k

   Recall, when discriminant, D > 0; the equation would result in two different real solutions.

   Therefore; 4 – 24k > 0

   -24k > -4

   k < 1 / 6.

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