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

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Question: If the quadratic equation x^2 + px + q = 0 has roots 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. Thus, p + q = -5 + 6 = 1.

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

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

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: Calculate the sum of the roots: 2 + 3 = 5.
Step 4: Now, apply the negative sign: p = -5.
Step 5: Next, use Vieta's formulas to find q. According to Vieta's, q is the product of the roots. So, calculate 2 * 3.
Step 6: Calculate the product of the roots: 2 * 3 = 6.
Step 7: Now, you have p = -5 and q = 6. Add these two values together: p + q = -5 + 6.
Step 8: Calculate the sum: -5 + 6 = 1.

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 derive coefficients from given roots.