+0

# A Problem Needing An Answer

0
497
1

Find the positive value of $n$ such that the equation $9x^2+nx+1=0$ has exactly one solution in $x$.

May 14, 2019

#1
+123
+4

Ima reformat da question right quick nawmsayn:

Find the positive value of $$n$$ such that the equation $$9x^2+nx+1=0$$ has exactly one solution in $$x$$.

When working with quadratic equations and the question mentions something about a number of solutions, we definitely want to use the discriminant $$b^2-4ac$$.

Let's review what the output of the discriminant tells you about the solutions to a quadratic equation.

If $$b^2-4ac > 0$$, there are two solutions.

If $$b^2-4ac = 0$$, there is one solution.

If $$b^2-4ac < 0$$, there are no solutions.

Since we want only one solution, we want $$b^2-4ac = 0$$. Where currently $$a = 9, b = n, c = 1$$

$$b^2 - 4ac = 0 \rightarrow n^2 - 4(9)(1) = 0\rightarrow n^2 = 36 \rightarrow n = \pm 6$$

The question asks for the positive value of $$n$$, therefore $$n = 6$$

May 14, 2019