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

1 Answer
sente
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 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

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