Grade 10 Math: Quadratic Equations, Graphs, and More Solving Quadratic Equations

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True or False? The following equation is the quadratic formula: $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

True
False
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Using the quadratic formula, find the roots for the following equation $$ x(10x - 1) = 2 $$

\(x = \frac{1}{2}\) or \(x = -\frac{2}{5}\)
\(x = \frac{3}{2}\) or \(x = -\frac{2}{5}\)
\(x = \frac{1}{2}\) or \(x = -\frac{4}{5}\)
\(x = \frac{1}{2}\) or \(x = \frac{2}{5}\)
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Using the quadratic formula, find the roots for the following equation $$ 4x^2 + 3x - 27 = 0 $$

\(x = \frac{1}{4}\) or \(x = -3\)
\(x = \frac{9}{4}\) or \(x = -3\)
\(x = \frac{9}{4}\) or \(x = -2\)
\(x = \frac{9}{4}\) or \(x = -1\)
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Using the quadratic formula, find the roots for the following equation $$ 15x^2 - 26x - 21 = 0 $$

\(x = \frac{1}{3}\) or \(x = -\frac{3}{5}\)
\(x = \frac{2}{3}\) or \(x = -\frac{3}{5}\)
\(x = \frac{7}{3}\) or \(x = -\frac{3}{5}\)
\(x = \frac{7}{3}\) or \(x = -\frac{3}{7}\)
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Using the quadratic formula, find the roots for the following equation $$ 2x^2-7x=5 $$

\(x = \frac{6\pm\sqrt{89}}{4}\)
\(x = \frac{5\pm\sqrt{89}}{4}\)
\(x = \frac{3\pm\sqrt{89}}{4}\)
\(x = \frac{7\pm\sqrt{89}}{4}\)
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Using the quadratic formula, find the roots for the following equation $$ 10x+4=3x^2 $$

\(x = \frac{5\pm\sqrt{37}}{3}\)
\(x = \frac{5\pm\sqrt{35}}{3}\)
\(x = \frac{3\pm\sqrt{37}}{3}\)
\(x = \frac{3\pm\sqrt{37}}{3}\)
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Using the quadratic formula, find the roots for the following equation $$ 14=4x^2-6x $$

\(x = \frac{1\pm\sqrt{65}}{8}\)
\(x = \frac{3\pm\sqrt{65}}{8}\)
\(x = \frac{2\pm\sqrt{65}}{8}\)
\(x = \frac{3\pm\sqrt{61}}{8}\)
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Using the quadratic formula, find the roots for the following equation $$ \frac{1}{6}x^2+\frac{4}{3}x-\frac{2}{3}=0 $$

\(x = -4\pm 2 \sqrt{5}\)
\(x = -4\pm 2 \sqrt{3}\)
\(x = -4\pm 2 \sqrt{4}\)
\(x = -2\pm 2 \sqrt{2}\)
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