Chapter 10: Q 278. (page 1236)

In the following exercises, solve by using the Quadratic Formula.
$5 z (z - 2) = 3$

Short Answer

Expert verified

The solutions are $z = \frac{5 - 2 \sqrt{10}}{5} a n d z = \frac{5 + 2 \sqrt{10}}{5} .$

Step by step solution

Given information.

The given equation is: $5 z (z - 2) = 3$

Use the quadratic formula.

The quadratic formula for the equation $a x^{2} + b x + c = 0 i s x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} .$

Now we compare the given equation with the standard form we get

$a = 5, b = - 10 a n d c = - 3 .$

Now we substitute these values in the quadratic formula.

$z = \frac{- (- 10) \pm \sqrt{{(- 10)}^{2} - 4 (5) (- 3)}}{2 (5)} z = \frac{10 \pm \sqrt{100 + 60}}{10} z = \frac{10 \pm \sqrt{60}}{10} z = \frac{10 \pm 4 \sqrt{10}}{10} z = \frac{5 \pm 2 \sqrt{10}}{5}$

The two solutions are $z = \frac{5 - 2 \sqrt{10}}{5} a n d z = \frac{5 + 2 \sqrt{10}}{5} .$

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In the following exercises, solve by using the Quadratic Formula.
$5 z (z - 2) = 3$

Short Answer

Step by step solution

Given information.

Use the quadratic formula.

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In the following exercises, solve by using the Quadratic Formula.5z(z−2)=3

Short Answer

Step by step solution

Given information.

Use the quadratic formula.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Geometry

Probability and Statistics

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, solve by using the Quadratic Formula.
$5 z (z - 2) = 3$