If the roots of the quadratic equation x^2 + px + q = 0 are -2 and -3, what is t

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Question: If the roots of the quadratic equation x^2 + px + q = 0 are -2 and -3, what is the value of p + q? (2019)

Options:

Correct Answer: -6

Exam Year: 2019

Solution:

Using Vieta\'s formulas, p = -(-2 - 3) = 5 and q = (-2)(-3) = 6. Therefore, p + q = 5 + 6 = 11.

If the roots of the quadratic equation x^2 + px + q = 0 are -2 and -3, what is the value of p + q? (2019)

If the roots of the quadratic equation x^2 + px + q = 0 are -2 and -3, what is the value of p + q? (2019)

Step 1: Identify the roots of the quadratic equation, which are given as -2 and -3.
Step 2: Use Vieta's formulas to find p. According to Vieta's, p is the negative sum of the roots. So, calculate -(-2 - 3).
Step 3: Simplify the calculation for p: -(-2 - 3) = -(-5) = 5.
Step 4: Now, use Vieta's formulas to find q. According to Vieta's, q is the product of the roots. So, calculate (-2)(-3).
Step 5: Simplify the calculation for q: (-2)(-3) = 6.
Step 6: Now, add p and q together: p + q = 5 + 6.
Step 7: Calculate the final result: 5 + 6 = 11.

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.