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.

How do you describe the nature of the roots of the equation 6x^2=2x-16x^2=2x-1?