Graphically the roots of the equations are those values on ...



Graphically the roots of the equations are those values on x-axis at which the graph of given function meets x-axis.

For example for the equation,

x2 – 3x+2 = 0, its roots are x = 2, 1.

If we draw the graph of f(x) = x2 – 3x+2, then we can observe that its graph meets x-axis at x = 2, 1 also. So these are called real roots as its graph meets real axis at real values of x =2, 1.

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Now come to the imaginary roots, consider the equation; x2+4 = 0, its roots are

x = ±√-2 = ±2i, where i =√-1 is an imaginary number.

If we observe the graph of g(x)= x2+4, then it can see that its graph does not meet the real axis that’ why we say that its solution does not exist(or real roots does not exist).

[pic]

But on the complex plane(not xy-plane)its graph meets the y-axis (imaginary axis) at x= ±2i. That’s why this function is said to have complex roots.

[pic]

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