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

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

Options:

Correct Answer: -7

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 equation x^2 + px + q = 0 are -2 and -3, what is the value of p + q?

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

Step 1: Identify the given quadratic equation, which is x^2 + px + q = 0.
Step 2: Note the roots of the equation, which are -2 and -3.
Step 3: Use Vieta's formulas to find p. According to Vieta's, p is the negative sum of the roots. So, calculate -(-2 - 3).
Step 4: Simplify the calculation: -(-2 - 3) = -(-5) = 5. Therefore, p = 5.
Step 5: Now, use Vieta's formulas to find q. According to Vieta's, q is the product of the roots. So, calculate (-2)(-3).
Step 6: Simplify the calculation: (-2)(-3) = 6. Therefore, q = 6.
Step 7: Now, add p and q together: p + q = 5 + 6.
Step 8: Simplify the addition: 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 a quadratic equation and how to find its roots.