There is no such thing as a quadric equation.
The nearest word is quartic which is an equation involving the fourth power of the independent variable. It is unlikely that you will have come across that. It is possible that you might be wanting to refer to a quadratic equation, which is the equation of a parabola. That being the case, they two represent the same thing.
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x = 4.74 or -2.74
A quadratic equation can have two real solutions, one real solution, or two complex solutions, none of them real.
Yes, it often does. If you use the discrimnant, and the answer is <0, there is no answer, if it equals 0, there is one answer, and if it is >0 there are 2 answers
When the equation is in one the following formats: ax2+ bx+c = 0 a(x+b)2+c = 0 (x+a)(x+b) = 0 than it is a quadric. It is also quadratic when x2 and only x2 is in it. example: x2 + 1= 0 and x2=0 are quadratic equations. However ax3+bx2+ cx+d =0 is not a quadratic, this is a cubic because of the x3 term, However you can use the quadric equation to find one of the two answers for it.
If you put the equation into standard form, ax2 + bx + c = 0, then the number and type of roots are determined by the expression b2 - 4ac - this is because in the quadratic equation, this appears under a radical sign. If this expression is...Positive: the equation has two real solutions.Zero: the equation has one solution, sometimes considered a "double root".Negative: the equation has two complex solutions.