Why there are usually two solutions in quadratic equations??

Question

Why there are usually two solutions in quadratic equations??

Answer 1

In general, the solutions to an equation of any type are the points in which the graph of the function cuts the x-axis. To better understand this, you could use a graphing calculator or math software to plot the graph.

Now, the function for the quadratic equation is a*X^2+b*X+c, where a,b and c are real numbers. According to a, one can have the graph differently placed. It sometimes doesn't intersect the X-axis at all; that happens when we have complex solutions. Sometimes, only the vertex touches the X-axis and then the two solutions are equal. But mostly, the parabola intersects the X-axis twice. As I cannot draw to explain better, you might want to have a look here -> http://en.wikipedia.org/wiki/Quadratic_e... to better understand the graph thing. I sure hope this was useful!

Good luck! ;)

Answer 2

Quadratics describe a simple curve, which can intersect the x-axis (in two places -- two roots), be tangent to it (one solution -- a double root), or miss it altogether (two imaginary roots).

Answer 3

A polynomial of order n has N solutions where N ≤ n.

Answer 4

The solution to a quadratic equation is where the graph crosses the x-axis.

The graph of a quadratic function is a parabola.

A parabola will normally cross the x-axis two times (not always, which is why you sometimes get no real solutions, or a repeated real solution)

Answer 5

Consider this equation, y=x^2 + 9 is really just asking when we plug in a number for X say 10 what number do we get out for Y.  

for X=10, Y=109;  

but we can also get Y=109 if we plug in X=-10.  Its just because you square a term so the negatives cancel out.  Pari M's answer is also good to note.

Answer 6

simple:

take y = 2x+5

it will have one solution b/c x is to the 1 power

take y = 2x^2 + 6

it will have two solutions b/c x is to the 2nd power

take y  = 3x^3 + 7

it will have three solutions b/c x is to the 3rd power

now you tell me which one have two solutions? the one with x^2 which just so happens to be quadradic! yay!

hope that helps