Vieta’s Formula in Quadratic Equations
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
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 .
By Viete’s formula,
We are asked to find the value of
by factoring special product.
We already have (a+b) we just to find
Going back here
Worked Problem 3:
Find the value of K such that the sum of the roots of quadratic is -2.
Let p and q are the roots of equation.
By Vieta’s formula,