This math topic focuses on understanding the relationship between the discriminant of a quadratic equation and the nature of its roots. It explores scenarios where the discriminant is greater than zero, indicating two real and distinct roots; less than zero, indicating two complex roots; and equal to zero, suggesting a repeated real root. Through problems, learners are tasked with identifying valid roots based on given discriminants, enhancing their grasp of the quadratic formula and discriminants in a practical context.

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 Root Example Worksheet

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Quadratic Discriminants - Greater/Lesser than Zero to Root Example
1
Which roots would be valid for a quadratic function with this discriminant?
A LaTex expression showing \Delta = 0
a A LaTex expression showing x=8.4 \\x=7.5 \\
b A LaTex expression showing x=-1.5 \\
c A LaTex expression showing x=\frac{4.9 \pm isquare root of 1.9}{8.4} \\
2
Which roots would be valid for a quadratic function with this discriminant?
A LaTex expression showing \Delta > 0
a A LaTex expression showing x=-1.15 \\x=1.15 \\
b A LaTex expression showing x=2.4 \\
c A LaTex expression showing x=\frac{1.2 \pm isquare root of 6.4}{1.9} \\
3
Which roots would be valid for a quadratic function with this discriminant?
A LaTex expression showing \Delta < 0
a A LaTex expression showing x=9.4 \\x=5.1 \\
b A LaTex expression showing x=8.3 \\x=8.8 \\
c A LaTex expression showing x=\frac{-0 \pm isquare root of 16}{-2} \\