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

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

Options:

Correct Answer: -5

Solution:

Using Vieta\'s formulas, p = -(2 + 3) = -5.

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

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

Step 1: Understand that the equation x^2 + px + q = 0 is a quadratic equation.
Step 2: Recognize that the roots of the equation are given as 2 and 3.
Step 3: Recall Vieta's formulas, which relate the coefficients of the polynomial to the sums and products of its roots.
Step 4: According to Vieta's formulas, the sum of the roots (2 + 3) is equal to -p.
Step 5: Calculate the sum of the roots: 2 + 3 = 5.
Step 6: Set up the equation: -p = 5.
Step 7: Solve for p by multiplying both sides by -1: p = -5.

Vieta's Formulas – Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots.