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+2x1=0
and
The second answer is 4x^22x+1=0
If one were to replace 0 with y with both answers, one would get 2 different graphs.

answers:
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.

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.

rotchm say: The so called 'general form' of a poly (usually) means that the leading coefficient is positive.
IOW, 4x^22x+1=0 would be the general form, and not 4x^2+2x1=0.

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.

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 nonzero number and get another valid answer.
Yes, they have different graphs, but they all have the same xintercepts, 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.

Paladin say: they would both have the same xintercepts; except in this case, the same complex solutions
