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We are given the cubic equation: $$ 2x^3 - 23x^2 + 82x - 78 = 0 $$ --- ### Step 1: General Formula for Discriminant of a Cubic Polynomial For a cubic equation of the form: $$ ax^3 + bx^2 + cx + d = 0 $$ The discriminant $\Delta$ is given by: $$ \Delta = 18abcd - 4b^3d + b^2c^2 - 4ac^3 - 27a^2d^2 $$ --- ### Step 2: Identify coefficients Given: $$ a = 2,\quad b = -23,\quad c = 82,\quad d = -78 $$ --- ### Step 3: Substitute into the _____ _____ ______ _____ __________ ________ __________ ___ __________ ____ ________.
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