This topic covers the relationship between the discriminant of a quadratic equation and the nature of its roots. It specifically focuses on determining if the quadratic function has real roots, complex roots, or a repeated real root based on the value of the discriminant (\(\Delta\)). The questions guide the learner to identify whether a discriminant being less than zero, greater than zero, or equal to zero correlates to having complex roots, two distinct real roots, or exactly one real root, respectively.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Quadratic Discriminants - Greater/Lesser than Zero to Count of Roots Worksheet

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Quadratic Discriminants - Greater/Lesser than Zero to Count of Roots
1
What type of roots would a quadratic function with this discriminant have?
A LaTex expression showing \Delta < 0
a
2 complex roots
b
1 real root
c
2 real roots
2
What type of roots would a quadratic function with this discriminant have?
A LaTex expression showing \Delta = 0
a
2 complex roots
b
1 real root
c
2 real roots
3
What type of roots would a quadratic function with this discriminant have?
A LaTex expression showing \Delta > 0
a
2 complex roots
b
1 real root
c
2 real roots