SOLUTION: Find all real values of K for which 3t^2-4t+k=0 has imaginary roots
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Find all real values of K for which 3t^2-4t+k=0 has imaginary roots
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Quadratics don't have imaginary roots, they have complex roots -- when they don't have real roots, that is.
When the discriminant is less than zero, the roots of a quadratic are a conjugate pair of complex roots. The discriminant of
So for your problem, the discriminant is:
If the roots are to be complex:
Just solve the inequality. Any value of k in the solution set will result in complex roots for your quadratic.
My calculator said it, I believe it, that settles it