If the quadratic equation x^2 + px + q = 0 has roots 3 and 4, what is the value

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Question: If the quadratic equation x^2 + px + q = 0 has roots 3 and 4, what is the value of p + q? (2023)

Options:

Correct Answer: 12

Exam Year: 2023

Solution:

Using Vieta\'s formulas, p = -(3 + 4) = -7 and q = 3 * 4 = 12. Therefore, p + q = -7 + 12 = 5.

If the quadratic equation x^2 + px + q = 0 has roots 3 and 4, what is the value of p + q? (2023)

If the quadratic equation x^2 + px + q = 0 has roots 3 and 4, what is the value of p + q? (2023)

Step 1: Identify the roots of the quadratic equation. The roots given are 3 and 4.
Step 2: Use Vieta's formulas to find p. According to Vieta's, p is the negative sum of the roots. So, p = -(3 + 4).
Step 3: Calculate the sum of the roots: 3 + 4 = 7.
Step 4: Find p: p = -7.
Step 5: Use Vieta's formulas to find q. According to Vieta's, q is the product of the roots. So, q = 3 * 4.
Step 6: Calculate the product of the roots: 3 * 4 = 12.
Step 7: Now, we have p = -7 and q = 12.
Step 8: Find p + q: p + q = -7 + 12.
Step 9: Calculate the sum: -7 + 12 = 5.

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 derive coefficients from given roots.