The values of '''a,b''' and '''c''' for which the roots are the roots real and distinct, real and distinct, imaginary could be found out through this geogebra applet.
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For ex: The values of '''a, b''' and '''c''' could be zero at the beginning. Then, retaining '''b'''=0 and '''c'''=0 the value of '''a''' could be increased to 1. The changes in the curve observed , the kind of roots obtained etc., with changes in the values of '''a,b''' and '''c''' could be some of the points of discussion in the classroom.