_investigating-the-nature-of-the-roots-of-a-quadratic.jpg "Investigating the nature of the roots of a quadratic from zero of the zero polynomial Video Screenshot Preview")
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⏲ Duration: 10 min 58 sec
✓ Published: 04-Sep-2013
✓ Published: 04-Sep-2013
Description:
We make use of tools available to us in GeoGebra to distinguish between a concave up quadratic from a concave down quadratic. We then proceed to vary the coefficients of the quadratic polynomial in x to understand what effect this has on the parabola. We make the important observation of the three cases of the determinant being positive, zero, or negative and connect it to the roots of the polynomial being real and distinct, real and duplicate or complex conjugates of each other. Along the way,
We make use of tools available to us in GeoGebra to distinguish between a concave up quadratic from a concave down quadratic. We then proceed to vary the coefficients of the quadratic polynomial in x to understand what effect this has on the parabola. We make the important observation of the three cases of the determinant being positive, zero, or negative and connect it to the roots of the polynomial being real and distinct, real and duplicate or complex conjugates of each other. Along the way,
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