If the quadratic equation x^2 + px + q = 0 has roots 3 and -2, what is the value

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Question: If the quadratic equation x^2 + px + q = 0 has roots 3 and -2, what is the value of p + q? (2023)

Options:

Correct Answer: 5

Exam Year: 2023

Solution:

Using Vieta\'s formulas, p = -(3 + (-2)) = -1 and q = 3 * (-2) = -6. Therefore, p + q = -1 - 6 = -7.

If the quadratic equation x^2 + px + q = 0 has roots 3 and -2, what is the value of p + q? (2023)

If the quadratic equation x^2 + px + q = 0 has roots 3 and -2, what is the value of p + q? (2023)

Step 1: Identify the roots of the quadratic equation, which are given as 3 and -2.
Step 2: Use Vieta's formulas to find p. According to Vieta's, p is the negative sum of the roots. So, calculate 3 + (-2) = 1.
Step 3: Since p is the negative of that sum, p = -1.
Step 4: Now, use Vieta's formulas to find q. According to Vieta's, q is the product of the roots. So, calculate 3 * (-2) = -6.
Step 5: Now that we have p = -1 and q = -6, add them together to find p + q. So, calculate -1 + (-6) = -7.

Vieta's Formulas – These formulas relate the coefficients of a polynomial to sums and products of its roots.
Quadratic Equations – Understanding the standard form of quadratic equations and how to manipulate them to find roots.