Chapter 4: Q. 26 (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 $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ .
$z^{2} = 4 (2 z - 3)$

Short Answer

Expert verified

The values of z are $z = 6$ and $z = 2$ .

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 $z^{2} = 4 (2 z - 3)$ which can also be written as $z^{2} - 8 z + 12 = 0$ .Using quadratic formula $z = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ , substitute 1 for a, -8 for b and 12 for c.

Put the values in the formula and get $z = \frac{- (- 8) \pm \sqrt{{(- 8)}^{2} - 4 \times (1) \times (12)}}{2 (1)}$ .

- Simplify for z

Simplify the expression for z.

$\begin{matrix} z = \frac{- (- 8) \pm \sqrt{{(- 8)}^{2} - 4 \times (1) \times (12)}}{2 (1)} \\ = \frac{8 \pm \sqrt{64 - 48}}{2} \\ = \frac{8 \pm \sqrt{16}}{2} \\ = \frac{8 \pm 4}{2} \end{matrix}$

Therefore, either $z = \frac{8 + 4}{2} = \frac{12}{2}$ or $z = \frac{8 - 4}{2} = \frac{4}{2}$ that is., either $z = 6$ or $z = 2$ .

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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 $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ .
$z^{2} = 4 (2 z - 3)$

Short Answer

Step by step solution

- Understand the concept used

- Substitute the values

- Simplify for z

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Solve each equation by factoring or by using the quadratic formula. The quadratic formula is:If ax2+bx+c=0, with a≠0, thenx=−b±b2−4ac2a.z2=4(2z−3)

Short Answer

Step by step solution

- Understand the concept used

- Substitute the values

- Simplify for z

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Applied Mathematics

Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

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 $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ .
$z^{2} = 4 (2 z - 3)$