We all know to solve quadratic equation. We also know how to find the nature of roots of quadratic equation – whether it’s real and distinct/equal or imaginary.
Another way to solve a polynomial equation is to plot it. The point at which the equation crosses x-axis will be the solution. Try plotting a handful of equations with GeoGebra to familiarize yourself with the idea.
Puzzle: For what values of n does the equation
Quora Questionhave real roots?
One way is to use determinant of the quadratic equation to find the values of n.
The challenges for you is:
- Solve the same problem by plotting it using GeoGebra or Desmos.
- Find a third way to solve the same problem.
Purpose of this puzzle is to familiarize ourself with different ways to solve a polynomial equations, often not covered in depth in classrooms.
Leave your observations below in the comments! Those who plotted it using any software successfully, feel free to share the link to your file below.
Mathematicos 
For
, we get real roots. This can be done by normal calculation/ Descartes rule of signs/ using Geogebra
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Can you describe how you did it with Descarte’s Rule?
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