Answer
Two distinct real solutions.
Work Step by Step
For $ax^{2}+bx+c=0$, we can find solutions using the
Quadratic formula: $\displaystyle \quad x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$.
The radicand in the formula is called the discriminant.
$D=b^{2}-4ac$
D is positive $\Rightarrow$ there are two distinct real solutions.
D is zero $\Rightarrow$ there is one (double) real solution.
D is negative $\Rightarrow$ two solutions, complex conjugates (not real).
---
Here,
$ 2x^{2}-11x+3=0\quad\rightarrow \left\{\begin{array}{l}
a=2\\
b=-11\\
c=3
\end{array}\right.$
$D=b^{2}-4ac=(-11)^{2}-4(2)(3)=121-24=97$
$D$ is positive $\Rightarrow$ two distinct real solutions.
