Given a quadratic equation , let *p *and *q* be the roots of this equation then, we can relate the sum of the roots as well as the product of the roots by the following formula. This is called Viete’s formula.

The following formula was discovered by François Viète. The formula is not just for quadratic but for other polynomial equations with higher degree but we will just deal with quadratic equations for now.

**Worked Problem 1:**

Let p and q be the roots of equation , what is the value of

Solution:

Using Viete’s formula, we know that

We are asked to find the value of the following

by common factor

**Worked Problem 2:**

Let a and b be the roots of equation . Find the value of .

Solution:

By Viete’s formula,

and

We are asked to find the value of

by factoring special product.

We already have (a+b) we just to find

Going back here

since

**Worked Problem 3:**

Find the value of K such that the sum of the roots of quadratic is -2.

Solution:

Let p and q are the roots of equation.

By Vieta’s formula,

sir dan wala ba sa cubic , quartic or even a general Vieta’s formula for all types of degree 🙂

We will discuss that shortly.