Q6. Solve each equation by factoring... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 4: Q6. (page 163)

Solve each equation by factoring or by using the quadratic formula. The quadratic formula is:
If $a x^{2} + b x + c = 0$ , with $a 鈮� 0$ , then $x = \frac{鈭� b 卤 \sqrt{b^{2} 鈭� 4 a c}}{2 a}$ .
$2 z^{2} + 7 z = 0$

Short Answer

Expert verified

The values of z are $x = 鈭� \frac{7}{2}$ and $z = 0$ .

Step by step solution

- Understand the concept used

If $a x^{2} + b x + c = 0$ , with $a 鈮� 0$ , then $x = \frac{鈭� b 卤 \sqrt{b^{2} 鈭� 4 a c}}{2 a}$ . Solving using factoring can be done by splitting the middle term of equation and then making groups and equating them to zero.

- Substitute the values

It is given that $2 z^{2} + 7 z = 0$ .Using quadratic formula $z = \frac{鈭� b 卤 \sqrt{b^{2} 鈭� 4 a c}}{2 a}$ , substitute 2 for a, 7 for b and 0 for c.

Put the values in the formula and get. $z = \frac{鈭� 7 卤 \sqrt{{(7)}^{2} 鈭� 4 脳 (2) 脳 (0)}}{2 (2)}$

- Simplify for z

Simplify the expression for z.

$\begin{matrix} z = \frac{鈭� (7) 卤 \sqrt{{(7)}^{2} 鈭� 4 脳 (2) 脳 (0)}}{2 (2)} \\ = \frac{鈭� 7 卤 \sqrt{49 鈭� 0}}{4} \\ = \frac{鈭� 7 卤 \sqrt{49}}{7} \\ = \frac{鈭� 7 卤 7}{4} \end{matrix}$

Therefore, either $z = \frac{鈭� 7 + 7}{4} = \frac{0}{4}$ or $z = \frac{鈭� 7 鈭� 7}{4} = \frac{鈭� 14}{4}$ that is., either $z = 0$ or $z = 鈭� \frac{7}{2}$ .