# The discriminant of a quadratic equation is negative. One solution is 3+4i . What is the other solution? A.4-3i B.3-4i C.4+3i D.-3+4i

► For instance, the quadratic equation:

x² – (6 + 4i)x + (9 + 12i) = 0

has for discriminant:

Δ = (6 + 4i)² – 4(9 + 12i) = 36 – 16 + 48i – 36 – 48i = -16

which is indeed negative.

Its solutions will then be:

x₁ = [(6 + 4i) + 4i]/2 = 3 + 4i

x₂ = [(6 + 4i) – 4i]/2 = 3

And the other solution here is 3.

► If you are not convinced, the quadratic equation:

x² – (6 + 5i)x + (5 + 15i) = 0

has for discriminant:

Δ = (6 + 5i)² – 4(5 + 15i) = 36 – 25 + 60i – 20 – 60i = -9

which is indeed negative.

Its solutions will then be:

x₁ = [(6 + 5i) + 3i]/2 = 3 + 4i

x₂ = [(6 + 5i) – 3i]/2 = 3 + i

And the other solution here is 3+i.

► In fact, every quadratic equation of the form:

x² – [6 + (4 + α)i]x + (3 + 4i)(3 + αi) = 0

where α is any real, has for discriminant:

Δ = [6 + (4 + α)i]² – 4(3 + 4i)(3 + αi)

= 36 – (4 + α)² + 12(4 + α)i – 36 + 16α – 12(4 + α)i

= 16α – (4 + α)²

= 16α – 16 – 8α – α²

= -16 + 8α – α²

= -(α – 4)²

WILL be negative.

Their solutions will then be:

x₁ = [ [6 + (4 + α)i] – (α – 4)i ]/2 = 3 + 4i

x₂ = [ [6 + (4 + α)i] + (α – 4)i ]/2 = 3 + αi

And the other solution will then be is 3+αi.

Since α can take any real value, you'll obtain an infinity of solutions of the form 3+αi.

► So conclusively:

If the discriminant of a quadratic is negative AND one of the solutions is 3+4i, the only thing we can say about the other solution is that its real part must be 3.

## Related Questions

Which ordered pair is a solution of the equation 2x − y = 9 (-4,1) (-2,5) (5,1) (6,-3)

So based on my solution, the correct answer would be the third option: (5,1)

So let us try to plug in the values.

2(5) - 1 = 9

10 -1 = 9

9 = 9

So this is the correct one. Hope this answers your question.

Solve the equation for y 2x+6y=13

2x+6y=13

Next, transfer 2x to the right side and it will look like this:

6y=13-2x

Now, divide both sides by 6, and it will look like this:

y=13-2x

--------

6

So, this is the final answer for y.

Hope this answers your question. Have a great day!

The y-coordinate of the y-intercept is the _____ term in the equation of the line.

**constant**.

I hope my answer helped you. Feel free to ask more questions. Have a nice day!

**Answer:**

A) -4c^2 + 4c + 6

**Step-by-step explanation:**

The given polynomial is 2 + 7c – 4c^2 – 3c + 4

Add the like terms.

2 + 4 + 7c - 3c -4c^2

= 6 + 4c - 4c^2

Write it in a standard form

= -4c^2 + 4c + 6

Answer is A) -4c^2 + 4c + 6

Hope this will helpful.

Thank you.

Now we'll plug in the numbers they give us into the formula:

y-4= 0(x+2).

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Which solution for the value of x in the figure below is incorrect? Explain.

When RHS is brought to the LHS

Subtraction and not addition should be done to find the solution for x.

I hope my answer has come to your help. God bless and have a nice day ahead!

Graph passes through the point (-1, 0).

Therefore, x = -1 and y = 0.

This is the only equation which is true for x = -1 and y = 0.

Therefore, the solution is

**Answer:**

Just took the test!!

**Step-by-step explanation:**

Look at the image down below!!

WILL UPVOTE! Which equation is related to 89 = x + 61? A. x = 150 B. 61 = 89 + x C. x = 28 D. x = 18

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**Answer:**

**Option (a) is correct.**

** The radius of circle with equation is 2 units.**

**Step-by-step explanation:**

Given : The equation of circle as

We haave to determine the radiusof th circle whose equation is given as .

Consider the gicen equation

The standard equation of circle with centre (h, k) and radius r is given by

Thus, Comparing the gicen equation h = 7 , k = 10 and r = 2

**Thus, The radius of circle with equation is 2 units.**

Wait short time for answer a

How many solutions does this system of equations have? exactly one none infinitely many exactly two

We need to see the graph in order to give you an answer

The solution of a+b>−4 is a>−9. What is the value of b?

Hope this helps. c:

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A+24=-15 how do you do this 1-step equation

We just want to get only A on the LHS and how much A is on the RHS.

A + 24 - 24 = -15 - 24 // we get rid of the +24 to only leave A and we do it on the other side because we always do that

A = -39

Give 3 ordered pairs that satisfy the equation y=12x

when x = 1...

y = 12(1)

y = 12

ordered pair: (1, 12)

when x = 0...

y = 12(0)

y = 0

ordered pair: (0, 0)

when x = 2...

y = 12(2)

y = 24

ordered pair: (2, 24)

Find the center and radius of the circle with equation (x+6)^2y+4)^2=36

3 ordered pairs that satisfy the equation y=12x

x= 0 y=12*0 y=0

x=1 y=12*1 y=12

x=2 y=12*2 y=24

The slope of diagonal AB is , _ and its equation _ is .

m=(y₂-y₁)/(x₂-x₁)

We have two points A(-2,-2) and B(2,-2); therefore the slope will be:

m=(-2+2)/(2+2)=0/4=0

slope-intercept form:

y=mx +b

m=slope

b=y-intercept =-2

y=0x-2

y=-2

**Answer: The slope of diagonal AB is 0 and its equation is y=-2**

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Lets say you had a sentence like five more than a number is ten

so we would write that as

n+5=10 (N-stands for numbers, The + Stands for More, 5 stand for five, The equal sign stands for Is and then we finally add 10 at the end

Hope this helps you Mia

53p + 45h = 784.10

just a matter of subbing and solving...

53(h - 11) + 45h = 784.10

53h - 583 + 45h = 784.10

98h = 784.10 + 583

98h = 1367.10

h = 1367.10/98

h = 13.95

p = h - 11

p = 13.95 - 11

p = 2.95

so paperbacks (p) are 2.95 a piece and hardbacks (h) are 13.95 a piece

f(x) = one fourth x2 or B

Select the correct solution set. -7x ≥ 56 {x | x ≤ -8} {x | x ≥ -8} {x | x ≥ 8}

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y = mx + b

slope(m) = 1

(2,-2)...x = 2 and y = -2

now we sub and find b, the y int

-2 = 1(2) + b

-2 = 2 + b

-2 - 2 = b

-4 = b

so ur parallel line is : y = x - 4

I don't know how to do equation

What is the slope of line with equation 2x+3y+6=0

Subtract the 3y from both sides:

-3y=2x+6

Divide by -3:

y=(2/-3)x+6

Answer:

Slope = 2/-3

15x+20y=1800

20y=1800-15x

y=(1800-15x)/20

Now, we insert this y into the original equation (substitution).

15x+20[(1800-15x)/2]=1800

Now we combine like terms and solve for x.

15x+(36000-300x/2)=1800

36000-300x/2=-15x+1800

36000-300x=-30x+3600

36000=270x+3600

32400=270x

x=120

So the x-intercept is 120. Now, we can either go through that long process again to find the y-intercept (which is really inefficient, and you probably won't have time to do so on a test), or we can just input the x value we got into the original equation.

15x+20y=1800

15(120)+20y=1800

1800+20y=1800

20y=0

y=0

I'm not 100% sure about the y being 0, but I'm pretty sure. Hope this helped.

a) 7:38 rounds to about 7:40, so 7:15-7:40 is 25 minutes. 25/5 is 5; 5*30=150 plates.

b) Not quite sure how to do this part...?

Let x=number of seconds spent working

x / 10 = how many plates she's washed.