How do you describe the nature of the roots of the equation #6x^2=2x-1#?

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Answer 1 · 2017-06-01T22:08:19

The roots are imaginary.

If a quadratic equation is in the form:

#ax^2+bx+c#

The discriminant is defined to be:

#b^2-4ac#

In this case:

#6x^2-2x+1=0#

#a=6#
#b=-2#
#c=1#

Substituting:

#(-2)^2-4(6)(1)#

#4-24#

#-20#

Since the discriminant is negative, there are no real-number solutions.

If the discriminant is positive, there are 2 distinct real-number solutions and if the discriminant is #0#, one repeated real-number solution.