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

1 Answer
Jul 15, 2016

Answer:

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#