The discriminant of a quadratic function describes the nature of its roots:
<u>negative</u>: two complex roots
<u>zero</u>: one real root (multiplicity 2)
<u>positive</u>: two distinct real roots.
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Your discriminant of -8 is <em>negative</em>, so it indicates ...
There are two complex roots
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<em>Additional comment</em>
We generally study polynomials with <em>real coefficients</em>. These will never have an odd number of complex roots. Their complex roots always come in conjugate pairs.
Since the liquid from the cylinder was transfered to the cone until the latter was full, then what remains in the cylinder is it's original volume minus the cone volume. So we have: