If the sum of the roots of the equation x^2 + px + q = 0 is 8 and the product is

If the sum of the roots of the equation x^2 + px + q = 0 is 8 and the product is 15, what is the value of p? (2023)

If the sum of the roots of the equation x^2 + px + q = 0 is 8 and the product is 15, what is the value of p? (2023)

Step 1: Understand that the equation x^2 + px + q = 0 is a quadratic equation.
Step 2: Recall that for a quadratic equation ax^2 + bx + c = 0, the sum of the roots is given by -b/a and the product of the roots is given by c/a.
Step 3: In our equation, a = 1, b = p, and c = q.
Step 4: Since the sum of the roots is 8, we can write the equation: -p/1 = 8.
Step 5: Simplifying this gives us -p = 8.
Step 6: To find p, we multiply both sides by -1, resulting in p = -8.
Step 7: Therefore, the value of p is -8.

Quadratic Equations – Understanding the relationship between the coefficients and the roots of a quadratic equation, specifically using Vieta's formulas.
Vieta's Formulas – Using Vieta's formulas to relate the sum and product of the roots to the coefficients of the polynomial.