This math topic focuses on understanding the discriminant (\(\Delta\)) of quadratic equations and its relationship to the nature of the roots. Specifically, it offers practice in identifying discriminant values that indicate whether a quadratic equation will have real roots. The problems pose questions where learners are to select discriminant values from given options that are consistent with quadratic functions possessing real roots—including discriminants of zero, which imply a real double root. Each problem presents three different discriminant values to evaluate.

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

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Quadratic Discriminants - Has Real Roots to Discriminant Value Worksheet

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Quadratic Discriminants - Has Real Roots to Discriminant Value
1
Which discriminant would be from a quadratic function that has real roots?
a A LaTex expression showing \Delta = -19
b A LaTex expression showing \Delta = 0
c A LaTex expression showing \Delta = 19
2
Which discriminant would be from a quadratic function that does NOT have real roots?
a A LaTex expression showing \Delta = -29
b A LaTex expression showing \Delta = 0
c A LaTex expression showing \Delta = 29
3
Which discriminant would be from a quadratic function that has real roots?
a A LaTex expression showing \Delta = -8
b A LaTex expression showing \Delta = 0
c A LaTex expression showing \Delta = 8
4
Which discriminant would be from a quadratic function that has real roots?
a A LaTex expression showing \Delta = -10
b A LaTex expression showing \Delta = 0
c A LaTex expression showing \Delta = 10
5
Which discriminant would be from a quadratic function that has real roots?
a A LaTex expression showing \Delta = -13
b A LaTex expression showing \Delta = 0
c A LaTex expression showing \Delta = 13
6
Which discriminant would be from a quadratic function that has real roots?
a A LaTex expression showing \Delta = -17
b A LaTex expression showing \Delta = 0
c A LaTex expression showing \Delta = 17
7
Which discriminant would be from a quadratic function that has real roots?
a A LaTex expression showing \Delta = -10
b A LaTex expression showing \Delta = 0
c A LaTex expression showing \Delta = 10
8
Which discriminant would be from a quadratic function that has real roots?
a A LaTex expression showing \Delta = -12
b A LaTex expression showing \Delta = 0
c A LaTex expression showing \Delta = 12