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What do roots mean in Math?
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What do roots mean in Math?
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| 28/12 2013 22:45
roots are the solutions when the function is set to zero. they are also sometimes called "zeros". on a graph, they are the x-intercepts. sometimes, the x-axis is not intercepted. in this case the roots are not real, but imaginary or complex. an example: y = x^2 + 1 there is no real value for x that will make y equal zero. but there are two complex roots: x^2 + 1 = 0 x^2 = -1 x = ±√-1 = ±i (i = imaginary number) we can work backwards to see an example of two distinct real roots. if the roots are 2 and 3, then: (x - 2)(x - 3) = 0 x^2 - 5x + 6 = 0 y = x^2 - 5x + 6 has to real distinct roots sometimes the roots are real and equal, such as: y = x^2 - 4x + 4 which is the same as: y = (x - 2)^2 so, the root x=2, occurs twice since the fundamental theorem of algebra is that the number of roots is indicated by the degree of the polynomial. (all quadratics are of degree 2, and must have 2 roots of some kind) I hope this helps! ;)
| 28/12 2013 23:12
For ecample,ax^2+bx+c=0(a≠0，a,b,c are real number), we can get the roots x of the equation, x=(-b±√(b^-4ac))/2a, If (b^2-4ac)≧0, x is real roots, otherwise is a imaginary roots. If (b^2-4ac)≠0, x is (-b-√(b^-4ac))/2a & (-b±√(b^-4ac))/2a, obviously they are different ,so x is distinct number, If (b^2-4ac)＞0, x is distinct real number, because√(b^2-4ac) is a real number
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