greg1313 said:What do you get when you expand (x - a)(x - b)?
MarkFL said:Here's another approach:
Suppose we have:
\(\displaystyle ax^2+bx+c=0\)
Them by the quadratic formula, we have that the sum $S$ of the roots is given by:
\(\displaystyle S=\frac{-b+\sqrt{b^2-4ac}}{2a}+\frac{-b-\sqrt{b^2-4ac}}{2a}=-\frac{b}{a}\)
Use this formula on the given quadratic...what do you find?
The "Sum of the Roots" refers to the sum of all the solutions or roots of a given polynomial equation. In other words, it is the total value obtained when all the roots of the equation are added together.
The "Sum of the Roots" can be calculated using the Vieta's formulas, which state that the sum of the roots of a polynomial equation is equal to the negative coefficient of the second highest degree term divided by the leading coefficient. For example, in the equation ax^2 + bx + c = 0, the sum of the roots is -b/a.
The "Sum of the Roots" is important in mathematics because it helps in solving polynomial equations and understanding the relationship between the roots and the coefficients of the equation. It also has applications in other areas of mathematics, such as graph theory and number theory.
Yes, the "Sum of the Roots" can be negative if the coefficients of the polynomial equation are not all positive. This can happen when there are both positive and negative roots, or when the sum of the roots is equal to zero.
The "Sum of the Roots" and the "Product of the Roots" are related through Vieta's formulas. The product of the roots is equal to the constant term divided by the leading coefficient, while the sum of the roots is equal to the negative coefficient of the second highest degree term divided by the leading coefficient. This relationship is important in solving polynomial equations and finding the missing roots.