We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

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

 May 14, 2019

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

15 Online Users