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 $a \neq 0$ , then $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ .
$2 z^{2} + 7 z = 0$

Short Answer

Expert verified

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

Step by step solution

- Understand the concept used

If $a x^{2} + b x + c = 0$ , with $a \neq 0$ , then $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ . 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 $z = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ , substitute 2 for a, 7 for b and 0 for c.

Put the values in the formula and get. $z = \frac{- 7 \pm \sqrt{{(7)}^{2} - 4 \times (2) \times (0)}}{2 (2)}$

- Simplify for z

Simplify the expression for z.

$\begin{matrix} z = \frac{- (7) \pm \sqrt{{(7)}^{2} - 4 \times (2) \times (0)}}{2 (2)} \\ = \frac{- 7 \pm \sqrt{49 - 0}}{4} \\ = \frac{- 7 \pm \sqrt{49}}{7} \\ = \frac{- 7 \pm 7}{4} \end{matrix}$