Viète's formula
Okay kiddo, Viète's formula is a fancy math equation that helps you find the answer when you multiply all the roots of a polynomial equation together. But wait, what's a polynomial? Well, it's just a fancy way of saying an equation with a bunch of terms that have different powers of x (like x^2 or x^3).
Now, when we solve a polynomial equation, we try to find the values of x that make the equation true. These values are called the "roots" of the equation. For example, if we have the equation x^2 - 5x + 6 = 0, the roots are 2 and 3 (because 2^2 - 5(2) + 6 = 0 and 3^2 - 5(3) + 6 = 0).
Viète's formula helps us find the answer when we multiply all the roots of an equation together. The formula says that if we have a polynomial of degree n (which means the highest power of x in the equation is n), then we can write the product of its roots as a fraction with two parts:
- The numerator is the constant term of the polynomial (which is just the plain number at the end of the equation).
- The denominator is the coefficient of the term with the highest power of x, but with the opposite sign.
Let's use the same example as before: x^2 - 5x + 6 = 0. This has degree 2, so we can use Viète's formula to find the product of its roots. The constant term is 6, and the coefficient of the x^2 term is 1 (because there's an invisible "1" in front of the x^2). So the denominator is -1. Now we just divide 6 by -1 to get -6, which is the product of the roots (because 2 times 3 is 6).
So that's it! Viète's formula is a way to find the product of all the roots of a polynomial equation by using the constant term and the coefficient of the highest power of x. Pretty cool, right?
Now, when we solve a polynomial equation, we try to find the values of x that make the equation true. These values are called the "roots" of the equation. For example, if we have the equation x^2 - 5x + 6 = 0, the roots are 2 and 3 (because 2^2 - 5(2) + 6 = 0 and 3^2 - 5(3) + 6 = 0).
Viète's formula helps us find the answer when we multiply all the roots of an equation together. The formula says that if we have a polynomial of degree n (which means the highest power of x in the equation is n), then we can write the product of its roots as a fraction with two parts:
- The numerator is the constant term of the polynomial (which is just the plain number at the end of the equation).
- The denominator is the coefficient of the term with the highest power of x, but with the opposite sign.
Let's use the same example as before: x^2 - 5x + 6 = 0. This has degree 2, so we can use Viète's formula to find the product of its roots. The constant term is 6, and the coefficient of the x^2 term is 1 (because there's an invisible "1" in front of the x^2). So the denominator is -1. Now we just divide 6 by -1 to get -6, which is the product of the roots (because 2 times 3 is 6).
So that's it! Viète's formula is a way to find the product of all the roots of a polynomial equation by using the constant term and the coefficient of the highest power of x. Pretty cool, right?