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Dividing by variable when solving algebraic equation
#11
RE: Dividing by variable when solving algebraic equation
(25th October 2016, 21:54)Fireball Wrote:
(25th October 2016, 08:13)robvalue Wrote: It may have a repeated solution, however. Some quadratic equations have no real solutions, but they all have at least one complex solution.

Could I have an example?

Any equation where the constant is positive will do.

E.g. x^2 + 4

Let's test where it intersects the x axis:

x^2 + 4 = 0

=> x^2 = -4

therefore, x = 2i
"It is the mark of an educated mind to be able to entertain a thought without accepting it" ~ Aristotle
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#12
RE: Dividing by variable when solving algebraic equation
(25th October 2016, 21:54)Fireball Wrote:
(25th October 2016, 08:13)robvalue Wrote: It may have a repeated solution, however. Some quadratic equations have no real solutions, but they all have at least one complex solution.

Could I have an example?

x^2 +2x + 1 = 0 => (x+1)^2 = 0 => x = -1 (repeated solution due to the left side of the original equation being a perfect square).

To be clear, repeated solution does not apply to the specific form of quadratic equation that Vic referred to: (i.e., x^2 = constant). Aside from when the constant is 0, there will always be two solutions to such an equation.
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#13
RE: Dividing by variable when solving algebraic equation
(25th October 2016, 21:58)FallentoReason Wrote:
(25th October 2016, 21:54)Fireball Wrote: Could I have an example?

Any equation where the constant is positive will do.

E.g. x^2 + 4

Let's test where it intersects the x axis:

x^2 + 4 = 0

=> x^2 = -4

therefore, x = 2i

Also x = -2i
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#14
RE: Dividing by variable when solving algebraic equation
(26th October 2016, 01:52)robvalue Wrote:
(25th October 2016, 21:58)FallentoReason Wrote: Any equation where the constant is positive will do.

E.g. x^2 + 4

Let's test where it intersects the x axis:

x^2 + 4 = 0

=> x^2 = -4

therefore, x = 2i

Also x = -2i

Oops, thanks for the correction!
"It is the mark of an educated mind to be able to entertain a thought without accepting it" ~ Aristotle
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#15
RE: Dividing by variable when solving algebraic equation
No worries, so easily done Smile

For the general equation

ax^2 + bx + c = 0

where a isn't zero, and a, b and c are real numbers:

you can calculate the value of

d = b^2 - 4ac

When d > 0 you have two real solutions
When d = 0 you have one real solution
When d < 0 you have two complex solutions

The solution(s) are given by

x = [ -b + sqrt(d) ] / 2a

and

x = [ -b - sqrt(d) ] / 2a

sqrt is square root. As you can see, when d = 0, these two solutions are the same. When d < 0 we're taking the square root of a negative number, and as such the result will be complex.

[If you allow a, b and c to be complex the solution formulae still work.]
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#16
RE: Dividing by variable when solving algebraic equation
Ah yeah, good old quadratic equation. Clearly I haven't touched it in a while Big Grin
"It is the mark of an educated mind to be able to entertain a thought without accepting it" ~ Aristotle
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#17
RE: Dividing by variable when solving algebraic equation
(26th October 2016, 01:52)robvalue Wrote:
(25th October 2016, 21:58)FallentoReason Wrote: Any equation where the constant is positive will do.

E.g. x^2 + 4

Let's test where it intersects the x axis:

x^2 + 4 = 0

=> x^2 = -4

therefore, x = 2i

Also x = -2i

And here I go with an imaginary heart attack.
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition

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#18
RE: Dividing by variable when solving algebraic equation
It's like classic Shakespeare Big Grin

Teacher: What is the square root of 4?

Pupil: Easy! 2!

Teacher: And...

Pupil: ...

Pupil: ...

Pupil: Oh, and minus 2!

Teacher: Too late. *Pulls out gun*
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#19
RE: Dividing by variable when solving algebraic equation
(26th October 2016, 02:14)FallentoReason Wrote: Ah yeah, good old quadratic equation. Clearly I haven't touched it in a while Big Grin

One of those things that's forever etched into my brain. I can't remember what I did five fucking minutes ago, but I can recite all that like a parrot.

I dare you to go look up the general solution to a cubic equation Tongue
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#20
RE: Dividing by variable when solving algebraic equation
(26th October 2016, 02:16)Alex K Wrote:
(26th October 2016, 01:52)robvalue Wrote: Also x = -2i

And here I go with an imaginary heart attack.

Would it kill you if I said I have an engineering degree...? *gulp!*

In my defence, I study architecture at the moment. Maybe maths just wasn't meant to be  Tongue
"It is the mark of an educated mind to be able to entertain a thought without accepting it" ~ Aristotle
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