﻿ Does this question have 2 answers? Find the quadratic equati - science mathematics

[From: Mathematics] [author: ] [Date: 01-07] [Hit: ]
Does this question have 2 answers? Find the quadratic equation in general form x(x+2) = 5x^2+1 ?Should there be 2 answers for any question like this? Like, for this example, The first answer is -4x^2+2x-1=0 and The second answer is 4x^2-2x+1......

Does this question have 2 answers? Find the quadratic equation in general form x(x+2) = 5x^2+1 ?
Should there be 2 answers for any question like this? Like, for this example,
and

If one were to replace 0 with y with both answers, one would get 2 different graphs.
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Jeffrey K say: Those equations are the same. Just multiply everything by -1.
Both equations have the same pair of solutions. If you graph them, one parabola will be an upside down copy of the other, but they will both have the same x intercepts.
The general form of a quadratic equation has a positive coefficient on the x^2 term.
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Krishnamurthy say: x(x + 2) = 5x^2 + 1
4x^2 - 2x + 1 = 0
Multiplying both sides of the equation by -1
we get what may be called the same equation.
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rotchm say: The so called 'general form' of a poly (usually) means that the leading coefficient is positive.
IOW, 4x^2-2x+1=0 would be the general form, and not -4x^2+2x-1=0.
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david say: What you have are 2 different forms of the same equation. No, there are not 2 answers, /// multiply one equation by -1 and it gives the other equation showing that they are the same equation.
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Jeff Aaron say: Yes, -4x^2 + 2x - 1 = 0 and 4x^2 - 2x + 1 = 0 are both valid answers. You can also multiply either equation through by any non-zero number and get another valid answer.

Yes, they have different graphs, but they all have the same x-intercepts, which is what matters if you're trying to find the roots/solutions.

The solutions are:
x = (-(-2) +/- sqrt((-2)^2 - 4*4*1)) / (2*4)
x = (2 +/- sqrt(4 - 16)) / 8
x = (2 +/- sqrt(-12) / 8
x = 0.25 +/- sqrt(-0.1875)
No real solutions.
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Paladin say: they would both have the same x-intercepts; except in this case, the same complex solutions
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