If the sum of the roots of the equation x^2 + px + q = 0 is 5 and the product is

If the sum of the roots of the equation x^2 + px + q = 0 is 5 and the product is 6, what are the values of p and q? (2023)

If the sum of the roots of the equation x^2 + px + q = 0 is 5 and the product is 6, what are the values of p and q? (2023)

Step 1: Understand that the equation x^2 + px + q = 0 is a quadratic equation.
Step 2: Recall Vieta's formulas, which relate the coefficients of the equation to the roots.
Step 3: Identify that the sum of the roots is given as 5.
Step 4: According to Vieta's formulas, the sum of the roots is equal to -p. So, we can write -p = 5.
Step 5: To find p, we solve -p = 5, which gives us p = -5.
Step 6: Next, identify that the product of the roots is given as 6.
Step 7: According to Vieta's formulas, the product of the roots is equal to q. So, we can write q = 6.
Step 8: Now we have found the values: p = -5 and q = 6.

Vieta's Formulas – These formulas relate the coefficients of a polynomial to sums and products of its roots.