# How do you use the discriminant to determine the nature of the solutions given  4y^2 – 12y + 9 = 0?

Jul 15, 2016

Note that the discriminant evaluates to $0$ and conclude that the equation has one real solution.

#### Explanation:

Noting that the given equation is of the form $a {y}^{2} + b y + c = 0$ with $a = 4$, $b = - 12$, and $c = 9$, we can use the discriminant ${b}^{2} - 4 a c$ to determine the number of real solutions the equation has.

As the discriminant in this case is ${b}^{2} - 4 a c = {\left(- 12\right)}^{2} - 4 \left(4\right) \left(9\right) = 0$, the equation has exactly one real solution. Using other methods such as factoring or the quadratic formula shows that the solution is $y = \frac{3}{2}$