2007-01-09 16:00:16 · 9 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
A quadratic equation has a graph of a parabola, which is the same shape as the path of water coming out of a water fountain. Since this path can cross the x-axis twice, there are usually two solutions. If the path touches the axis just once, there is one solution; if it does not cross the axis, there is no solution.
2007-01-09 16:04:36 · answer #1 · answered by Albertan 6 · 1⤊ 0⤋
There are ALWAYS two solutions to a quadratic equation, although it may happen that the two have the same value. In general, there are N solutions to an equation of the Nth degree. To see this, consider:
(x-r1)(x-r2)(x-r3)... = 0 for N factors. The degree of the expression is N, and all of the rN are roots.
2007-01-09 16:06:52 · answer #2 · answered by Anonymous · 0⤊ 0⤋
There are always two solutions to a quadratic equation. One may be a negative root or imaginary number. But this is one of the fundamental rules of algebra. A negative number squared is a real number.
2007-01-09 16:15:13 · answer #3 · answered by richard Alvarado 4 · 0⤊ 0⤋
not usually but always as the no. of solutions to a equation is equal to the total of exponents/powers of all the variables in the equation.
& a quadratic equation is a second degree equation, hence two roots.
2007-01-09 16:06:13 · answer #4 · answered by ? 4 · 1⤊ 0⤋
A quadratic has two real solutions if it hits the x-axis twice. It has two imaginary solutions if it doesn't touch the x-axis at all. The only other case is that it touches the x-axis once so it has one real solution.
2007-01-09 16:21:11 · answer #5 · answered by Professor Maddie 4 · 1⤊ 0⤋
the key is in the quadratic equation
here is the link:
http://mathworld.wolfram.com/QuadraticEquation.html
since the equation starts with -b +/-... it means you have to solve for -b PLUS (the rest of the equation) and also -b MINUS (the rest of the equation.
unless the "rest of the equation" is zero, there will always be 2 solutions
2007-01-09 16:06:59 · answer #6 · answered by cardboard cowboy 5 · 0⤊ 0⤋
A quadratic always has two solutions although they may real or imaginary.
2007-01-09 17:00:33 · answer #7 · answered by futureastronaut1 3 · 0⤊ 0⤋
well, when you solve for x, you are usually left with "x^2 = ....". so when you take the square root of it, you get two solutions-- the positive and the negative. y is can be the same for two different values of x because of this, which causes two solutions graphically.
2007-01-09 16:05:02 · answer #8 · answered by car of boat 4 · 0⤊ 0⤋
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2015-12-28 17:52:01 · answer #9 · answered by NONAME 1 · 0⤊ 0⤋