What is the discriminant of #f(x)=-3x^2-2x-1#?

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Answer 1 · 2014-09-11T05:29:18

Please see the following link to learn how to find the discriminant.

Answer 2 · 2015-08-02T08:19:20

The discriminant is #-8#

#f(x) = -3x^2-2x-1# is of the form #ax^2+bx+c#,

with #a=-3#, #b=-2# and #c=-1#

The discriminant #Delta# is given by the formula:

#Delta = b^2 - 4ac#

#= (-2)^2-(4xx-3xx-1) = 4-12 = -8#

The discriminant is the expression under the square root in the quadratic formula for the solutions of #ax^2+bx+c = 0#, viz

#x = (-b+-sqrt(b^2-4ac))/(2a) = (-b+-sqrt(Delta))/(2a)#

In our case #Delta = -8 < 0#, so the square root has a pure imaginary value and the solutions of #f(x) = 0# are complex conjugates.