It would be easier using the quadratic formula instead of Vieta's ones for proving b).sooyong94 said:Homework Statement
Part (b)
Homework Equations
Vieta's formula
The Attempt at a Solution
Part (a):
I'm kinda stuck on part (b) - I tried multiplying the product of roots and got b^2 d^2, but I have no idea on dealing with the sum of roots.
Vieta's formula, also known as Vieta's relations or Vieta's theorem, is a mathematical equation that relates the coefficients of a polynomial to its roots. It is named after French mathematician François Viète.
Vieta's formula is used to find the sum and product of the roots of a polynomial equation. It can also be used to find the coefficients of a polynomial if the roots are known.
Vieta's formula is significant because it provides a quick and efficient way to find the sum and product of polynomial roots, which are important in various areas of mathematics, such as algebra, calculus, and number theory.
Vieta's formula has many applications in mathematics, including solving polynomial equations, determining the properties of conic sections, and finding the roots of a polynomial in complex numbers. It is also used in physics and engineering to solve problems related to vibrations and waves.
Yes, Vieta's formula only applies to polynomial equations, and it does not work for equations with irrational or imaginary roots. It also does not work for equations with multiple variables or equations that are not in standard form.