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?

Options:

Correct Answer: 5

Solution:

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

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

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

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, which state that for a quadratic equation ax^2 + bx + c = 0, the sum of the roots (r1 + r2) is equal to -b/a.
Step 4: In our equation, a = 1 (the coefficient of x^2), b = p, and c = q.
Step 5: Calculate the sum of the roots: -2 + (-3) = -5.
Step 6: According to Vieta's formulas, -b/a = -5. Since a = 1, we have -p = -5.
Step 7: Solve for p: p = 5.

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