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lara [203]
3 years ago
7

When the solutions are going to be complex, which methods can be used to solve quadratic equations?

Mathematics
1 answer:
yKpoI14uk [10]3 years ago
7 0
You could complete the square to state the vertex. 
You could use the quadratic equation to find the roots (which are complex). 

Try an example that will require both.

y = x^2 + 2x + 5

Step One
Get the graph. That's included below.

Step Two
Provide the steps for completing the square.
Note: we should get (-1,4)

y= (x^2 +2x ) + 5
y = (x^2 +2x + 1) + 5 - 1
y = (x +1)^2 + 4

The vertex is at (-1,4)

Step Three
Find the roots. Use the quadratic equation. Note that the graph shows us that the equation never crosses or touches the x axis. The roots are complex.

\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a}

a = 1
b = 2
c = 5

\text{x = }\dfrac{ -2 \pm \sqrt{2^{2} - 4*1*5 } }{2}
\text{x = }\dfrac{ -2 \pm \sqrt{4 - 20 } }{2}
\text{x = }\dfrac{ -2 \pm \sqrt{-16 } }{2}
\text{x = }\dfrac{ -2 \pm 4i }{2}
x = -1 +/- 2i

x1 = -1 + 2i
x2 = -1 - 2i And we are done.


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Factor (16a2 - 49) completely
riadik2000 [5.3K]

Answer:

(4a+7)(4a-7)

Step-by-step explanation:

5 0
3 years ago
The school that molly goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 6 sen
krek1111 [17]
The cost of a senior citizen ticket is $15 and the cost of a student ticket is $12.

How did I get this?
We know that 6 citizen tickets and 7 student stickers sold for $174 the first day. And 10 citizen tickets and 14 student tickets sold for $318 the second day.

1. create two equations out of this: C= citizen cost per ticket and S = student cost per ticket.

  6C + 7S = $174
10C + 14S = $318

2. Use process of elimination. Multiply the first equation by 2 because we want two variables to cancel out.

-12C - 14S = -$348
10C + 14S = $318
Combine like terms.

-2C = $30
Divide by -2 on both sides. The left side cancels out.

C = $30/-2
C = -$15 (In this case the negative doesn't matter)

C = $15 (cost of senior citizen ticket)

Plug the value of C into any of the two equations so we can get the value of S.

6($15) + 7S = $174
Distribute the 6 into the parenthesis.

$90 + 7S = $174
Subtract both sides by $90 and the left side will cancel out.

7S = $84
Divide both sides by 7.
S = $12

Student ticket: $12
Senior citizen ticket: $15




5 0
3 years ago
Please help!!!!!!!!!!
Delicious77 [7]

f(x)=2x^2-4x+1

Substitute the values of x to the equation of the function f:

x=-1\to f(-1)=2(-1)^2-4(-1)+1=2(1)+4+1=7\\\\x=2\to f(2)=2(2^2)-4(2)+1=2(4)-8+1=1

Therefore we have two points (-1, 7) and (2, 1).

We can calculate the slope of line l.

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

Substitute:

m=\dfrac{1-7}{2-(-1)}=\dfrac{-6}{3}=-2

<h3>Answer: A) -2.</h3>
5 0
3 years ago
How do you simplify 14/24
Bond [772]

Answer:

7/12

Step-by-step explanation:

Simplification is something we can do if both the numerator and denominator are divisible by the same number.

In 14/24, both numbers are divisible by 2.

So, we divide both the numerator and denominator by 2. We get 7/12.

Therefore 14/24 = 7/12.

7 0
3 years ago
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Answer:

Q1) Answer: After 3 minutes there will be 4.8 gallons of water in the fish tank. Q2) Answer: 40 gallons of water will be filled after 25 minutes.

8 0
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