For ax^2 + bx +c = 0,

**x = [ -b +/- sqrt( b^2 - 4ac)]/2a <--Quadratic formula**.

Example: Use quadratic formula to solve for the roots of

x^2 - x - 6 = 0

We identify a, b and c: a = 1, b = -1 and c = -6.

Applying the formula:

x = [ -(-1) +/- sqrt( (-1)^2 - 4(1)(-6)]/2(1)

-(-1) = 1 and (-1)^2 = 1 (since negative times negative is positive)

So,

x = [ 1 +/- sqrt(1 + 24)]/2

= [ 1 +/- sqrt(25)]/2

= [ 1 +/- 5 ]/2 since sqrt(25) = 5.

We can write that with as, x = (1 + 5)/2 ; x = (1 - 5)/2

For x = (1 + 5)/2

= 6/2 = 3

For x = (1 - 5)/2

= -4/2 = -2

Hence **roots are 3 and -2**.

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