Nature of Roots

THE SUM AND PRODUCT OF ROOTS.

Mr. Clark taught us how the sum and product of roots are related to the quadratic equation.

But before talking about that... how can we get the roots? Well, we can get the roots of a quadratic by:

1.) factoring

2.) using the quadratic formula

3.) or completing the square.

For most of us factoring is the easiest way to get the root.

(factoring review? *click here)

(the quadratic formula?*click here)

(forgot how to complete the square?*click here)

When a (leading coefficient) is 1:

the sum of the roots is the negative or the opposite of b (coefficient of x)

the product of the roots is the c (constant term)

Example #1)

If the roots are 4 and 8,then the quadratic is

.

The b (coefficient of x) is −(12), which is the negative of the sum of the roots. The c (constant term) is 32, which is their product.

Example #2)

a = 1; b = -2; c = -15

Sum of the roots is -b/a = -(-2)/1 = 2
Product of the roots is c/a = -15/1 = -15

That`s all for now. CIAO! :)

oh yah... ANNNNND tomorrow's scribe is Jamilyn G. ^_^