Question

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

Answer 1

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 `ay^2+by+c=0` with `a=4`, `b=-12`, and `c=9`, we can use the discriminant `b^2-4ac` to determine the number of real solutions the equation has.

As the discriminant in this case is `b^2-4ac = (-12)^2-4(4)(9) = 0`, the equation has exactly one real solution. Using other methods such as factoring or the quadratic formula shows that the solution is `y=3/2`