Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 10 - Quadratic Equations - 10.3 - Quadratic Formula - Concept Quiz 10.3: 4

Answer

True

Work Step by Step

The equation $x^{2}+4x=0$ is actually $x^{2}+4x+0=0$ as its constant is zero. Since $x^{2}+4x+0=0$ is in the standard form of the quadratic equation $ax^{2}+bx+c=0$, it can be solved by the quadratic formula. We now solve this equation through the quadratic formula to illustrate our conclusion: Step 1: Comparing $x^{2}+4x+0=0$ to the standard form of a quadratic equation $ax^{2}+bx+c=0$: $a=1$, $b=4$, and $c=0$ Step 2: The quadratic formula is: $x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$ Step 3: Substituting the values of a, b and c in the formula: $x=\frac{-(4) \pm \sqrt {(4)^{2}-4(1)(0)}}{2(1)}$ Step 4: $x=\frac{-4 \pm \sqrt {16+0}}{2}$ Step 5: $x=\frac{-4 \pm \sqrt {16}}{2}$ Step 6: $x=\frac{-4 \pm 4}{2}$ Step 7: $x=\frac{-4+4}{2}$ or $x=\frac{-4-4}{2}$ Step 8: $x=\frac{0}{2}$ or $x=\frac{-8}{2}$ Step 9: $x=0$ or $x=-4$ Step 10: Therefore, the solution set is {$-4,0$}. Therefore, the question statement is true.
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