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

Jun 1, 2017

The roots are imaginary.

#### Explanation:

If a quadratic equation is in the form:

$a {x}^{2} + b x + c$

The discriminant is defined to be:

${b}^{2} - 4 a c$

In this case:

$6 {x}^{2} - 2 x + 1 = 0$

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

Substituting:

${\left(- 2\right)}^{2} - 4 \left(6\right) \left(1\right)$

$4 - 24$

$- 20$

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.