For this case we have that by definition, the roots, or also called zeros, of the quadratic function are those values of x for which the expression is 0.

Then, we must find the roots of:

$2x ^ 2-4x + 5 = 0$

Where:

$a = 2\\b = -4\\c = 5$

We have to: $x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}$

Substituting we have:

$x = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (2) (5)}} {2 (2)}\\x = \frac {4 \pm \sqrt {16-40}} {4}\\x = \frac {4 \pm \sqrt {-24}} {4}$

By definition we have to:

$i ^ 2 = -1$

So:

$x = \frac {4 \pm \sqrt {24i ^ 2}} {4}\\x = \frac {4 \pm i \sqrt {24}} {4}\\x = \frac {4 \pm i \sqrt {2 ^ 2 * 6}} {4}\\x = \frac {4 \pm 2i \sqrt {6}} {4}\\x = \frac {2 \pm i \sqrt {6}} {2}$

Thus, we have two roots:

$x_ {1} = \frac {2 + i \sqrt {6}} {2}\\x_ {2} = \frac {2-i \sqrt {6}} {2}$

Answer:

$x_ {1} = \frac {2 + i \sqrt {6}} {2}\\x_ {2} = \frac {2-i \sqrt {6}} {2}$

3 0

4 years ago

On a map, 1 in. represents 12 mi. Two cities are 6 1/2in. apart on the map.

olasank [31]

1 inch = 12 miles

so 6 1/2 inches (or 6.5 inches) = 6.5 * 12 = 78 miles <===

7 0

4 years ago

Read 2 more answers

A local store buys used video games. For each game bought, they would pay $18 less than the original price paid for the game. Wh

Sonbull [250]

Answer:

total amount = n (d-18)

total amount = dn - 18n

Step-by-step explanation:

given data

pay = $18 less than the original price

originally cost = d dollars

sell = n games

solution

we take original price paid for the game = d

and they will pay $18 less than the original price

so that can we say

d -18

and

when sold n games than the cost of n used games will be here

cost = n (d-18)

so it can express as

total amount = n (d-18)

total amount = dn - 18n

7 0

3 years ago

Given h(x) = -5x + 3, find h(5).

cluponka [151]

Answer:

h(5) = -22

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Function Notation

Step-by-step explanation:

Step 1: Define

h(x) = -5x + 3

h(5) is x = 5

Step 2: Evaluate

Substitute in x [Function]: h(5) = -5(5) + 3
Multiply: h(5) = -25 + 3
Add: h(5) = -22

8 0

3 years ago