What are roots?how would you find the roots of an eaquations graphically and algebraically? give an example for each

Roots of a function f(x) are the values of x for which
f(x) = 0.

To find the roots graphically we plot the graph
f(x) versus x and find the points where the graph intersects the x-axis. The value of x
at these points if substituted in f(x) gives
0.

Algebraically, roots can be found by solving the
equation f(x) = 0.

For some forms like quadratic and cubic
equations you have standard formulae for the roots. For higher order equations
factorization has to be used. And they have to be reduced in
order.

Example: For the function f(x) = x^2 - 2x - 3, the
roots can be found by solving x^2 - 2x - 3 = 0

=>
x^2 - 3x + x - 3 = 0

=> x(x - 3) + 1(x - 3) =
0

=> (x + 1)(x - 3) =
0

The roots we get are x = -1 and
+3

If the graph y = x^2 - 2x - 3 were to be plotted we
would find the graph intersecting the x-axis at x = -1 and x =
3.