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# 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

The way you stated the problem, there is an infinity of possibilities for the other solution.

► 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

Posted in Mathematics

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

In order to confirm if which ordered pair is a solution of the given equation above, we can just simply plug in the values.
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

Posted in Mathematics

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

So here is how we are going to solve for y for the given equation above:
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.

Posted in Mathematics

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

For the answer to the missing term in the question above, the question is as simple as its answer. The right answer is constant.
I hope my answer helped you. Feel free to ask more questions. Have a nice day!

Posted in Mathematics

When simplified and written in standard form, which quadratic function is equivalent to the polynomial shown? 2 + 7c – 4c2 – 3c + 4 –4c2 + 4c + 6 –7c2 + 10c + 6 –4c2 + 4c + 8 –7c2 + 7c + 6

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

Step-by-step explanation:

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

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

Thank you.

Posted in Mathematics

What is the equation in point slope form of the line that passes through the point (–2, 4)(–2, 4) and has a slope of 5?

Point-slope formula: y-y1=m(x-x1)
Now we'll plug in the numbers they give us into the formula:

y-4= 0(x+2).

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Posted in Mathematics

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

The b is incorrect

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!

Posted in Mathematics

What is the equation of the following graph in vertex form? parabolic function going down from the left and turning at the point negative one comma zero and going up through the point zero comma one and continuing towards infinity Courtesy of Texas Instruments y = (x − 1)2 y = (x − 1)2 + 1 y = (x + 1)2 − 1 y = (x + 1)2

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 Posted in Mathematics

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

C! x = 28. If you use simplification, and then you find the answer and use it in the equation, it would be correct.

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What is the radius of a circle whose equation is (x – 7)2 + (y – 10)2 = 4? 2 units 4 units 8 units 16 units

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.

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Posted in Mathematics

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

You must do to the left hand side what you do to the right hand side.

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

Posted in Mathematics

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

To find ordered pairs that fit this equation, you just have to choose an x-value then record the answer for your y-value. you can literally go for anything you want, but it's easiest to pick smaller values:

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)

Posted in Mathematics

3 ordered pairs that satisfy the equation y=12x

(0, 0), (1, 12), (2, 24)
x= 0 y=12*0 y=0
x=1 y=12*1 y=12
x=2 y=12*2 y=24

Posted in Mathematics

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

Given two points (x₁,y₁) and (x₂,y₂) the slope of the line that passes through theses points will be:
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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Posted in Mathematics

When translating English sentences into math equations, the word is usually translates to which math symbol?

Ok how you Translating English into math equation here's an Example down below⬇

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

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Posted in Mathematics

I don't know how to do equation

Ok , so  your equation would be 14+.22x=16.20. just find x

Posted in Mathematics

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

You have to put in y=mx+b form, m is the slope.

Subtract the 3y from both sides:
-3y=2x+6

Divide by -3:
y=(2/-3)x+6

Slope = 2/-3

Posted in Mathematics

The total cost for Saturday's shipment, \$1800, is represented by the equation 15x+20y=1800. Help me intercepts X- and y- intercepts

You could find the x and y-intercepts by isolating these variables on one side. We'll start by finding y.

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.

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