This math topic focuses on using the quadratic formula to find the complex roots of quadratic equations. It explores how to determine the solutions of various quadratic equations when the discriminant results in negative values, leading to complex numbers as roots. Learners are tasked with analyzing each equation, using the quadratic formula appropriately, and understanding the representation of complex solutions in the form of \(x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}\), identifying both the real and imaginary parts of the solutions. This helps in deepening the understanding of discriminants and their implications on the nature of roots in quadratic equations.

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Quadratic Formula - Equation to Complex Roots Worksheet

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Quadratic Formula - Equation to Complex Roots
1
What roots (solutions) would this quadratic equation have?
A LaTex expression showing y=-5x to the power of 2 -3x-4
a A LaTex expression showing x=\frac{3 \pm isquare root of 71}{-10} \\
b A LaTex expression showing x=\frac{4.4 \pm isquare root of 7.7}{1.3} \\
2
A LaTex expression showing y=3x to the power of 2 +3
What roots (solutions) would this quadratic equation have?
a A LaTex expression showing x=\frac{-0 \pm isquare root of 36}{6} \\
b A LaTex expression showing x=\frac{1.7 \pm isquare root of 4.6}{8.2} \\
3
A LaTex expression showing y=3x to the power of 2 -x+1
What roots (solutions) would this quadratic equation have?
a A LaTex expression showing x=\frac{9.9 \pm isquare root of 3}{7.2} \\
b A LaTex expression showing x=\frac{1 \pm isquare root of 11}{6} \\
4
What roots (solutions) would this quadratic equation have?
A LaTex expression showing y=4x to the power of 2 +4x+4
a A LaTex expression showing x=\frac{7.1 \pm isquare root of 2.6}{1.7} \\
b A LaTex expression showing x=\frac{-4 \pm isquare root of 48}{8} \\
5
What roots (solutions) would this quadratic equation have?
A LaTex expression showing y=-4x to the power of 2 +2x-1
a A LaTex expression showing x=\frac{4 \pm isquare root of 3.5}{8.4} \\
b A LaTex expression showing x=\frac{-2 \pm isquare root of 12}{-8} \\
6
What roots (solutions) would this quadratic equation have?
A LaTex expression showing y=-1x to the power of 2 -2x-5
a A LaTex expression showing x=\frac{7.2 \pm isquare root of 4.3}{3.8} \\
b A LaTex expression showing x=\frac{2 \pm isquare root of 16}{-2} \\
7
What roots (solutions) would this quadratic equation have?
A LaTex expression showing y=4x to the power of 2 +2x+2
a A LaTex expression showing x=\frac{-2 \pm isquare root of 28}{8} \\
b A LaTex expression showing x=\frac{1.5 \pm isquare root of 4.6}{2.4} \\
8
What roots (solutions) would this quadratic equation have?
A LaTex expression showing y=-4x to the power of 2 -2x-3
a A LaTex expression showing x=\frac{5.5 \pm isquare root of 8.2}{1.7} \\
b A LaTex expression showing x=\frac{2 \pm isquare root of 44}{-8} \\