Math – Exercise 2 (Analysis)

Given

\(ax^2-5x+2=0\)

Find

All a that this equation has only one solution.

Solution

\(
\begin{array}{l}
\text{A linear equation has just one solution,} \\
\text{if the gradient isn’t zero.}\\
a_1=0 \\\\
\text{A quadratic equation has just one solution,} \\
\text{if}\ b^2-4ac=0\ \text{for}\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\ \text{(quadratic formula)}. \\
25-8a_2=0 \\
a_2=\frac{25}{8}
\end{array}
\)

Answer

\(a_1=0,\ a_2=\frac{25}{8}\)