Answer:
2 distinct real solutions
Step-by-step explanation:
The discriminant test allows us to figure out the number of solutions of a quadratic based on the sign the formula gives us after we plug in the respective values.
[tex]\[\boxed{\text{Discriminant Test Formula:}}\]\\\\D = b^2 - 4ac\\\\\text{Where:}\begin{itemize} \item \( a \) is the coefficient of \( x^2 \), \item \( b \) is the coefficient of \( x \), \item \( c \) is the constant term.\end{itemize}[/tex]
If D > 0: The quadratic equation has two distinct real solutions.
If D = 0: The quadratic equation has exactly one real solution.
If D < 0: The quadratic equation has no real solutions.
Solving:
[tex]\text{Given:}\ a = -24 \), \( b = -17 \), \( c = 20 \)\\\\D = (-17)^2 - 4(-24)(20) \\\\ D = 289 + 1920 \\\\\boxed{D = 2209 }[/tex]
Since D > 0 the quadratic equation has two distinct real solutions
