Potential roots have the format
factors of the constant term
-------------------------------------
factors of the initial term
Here, 7/3 is the only possible root that has a 7 in the numerator and a factor of 9 in the denominator.
Verify that 7/3 is a root using synthetic division.
It bears repeating: you should have applied the well-known following formulas: "Hello", "Please" and "Thanks".
Anyway...
= = = = = = = = = = = = = = = = = =
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.
Regards, to lizard squad >:0
Answer:
13,087 = 3x + 7,594
Step-by-step explanation:
have a good day
I am not for sure but I think 1.13*10-4
4( y-3) +9y is equal to:
Using ditributive property,
4 * y = 4y
4 * 3 = 12
Its equal to:
4y - 12 + 9y
Its also equal to:
9y + 4y = 13y
13y - 12