Alphabet

Alpha & Beta. The first two letters of the Greek alphabet. Why do we use them? Because we want to differentiate them from the other letters.

They are used to represent roots of a quadratic equation. if (x-5)(x-4)=0, then the roots are 5 & 4. (But you already knew that, don't you?)

Sometimes roots are difficult to find. Sometimes they are complex. But their sum and product is still real! Amazing? Not so. They are just some properties of a quadratic equation.

Let this general equation of roots A & B (alpha and beta hard to compute here...) be y = ax² + bx + c.

The sum of roots, A+B = -b/a.
The product of roots, AB = c/a

Basically everything else is a combo of the 2.

A²+B² =(A+B)² - 2AB

A²B+B²A = (A+B)AB

etc...

Bonus Question: This is from your textbook. (A^4)+(B^4) = ?
Remember A^4 means A to the power of 4.

What about Questions that asks you to form new equations with new roots? like roots 4A, 4B?

Well, you must first remember that all quadratic equations have the properties mentioned above.

 So let this equation be x²+hx+k = 0
Sum of roots 4A+4B = -h/1
Product of roots (4A)(4B)=k/1

Substitute the values in again to get h & k...then you'll get the new equation!

That is the crux of this part. Difficult at first, however this will soon become a breeze.