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For the equation x^2 + px + q = 0, if the roots are -2 and -3, what is the value

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

Options:

  1. 5
  2. 6
  3. 7
  4. 8

Correct Answer: 5

Solution: 

The sum of the roots is -(-2) + -(-3) = 5, hence p = 5.

For the equation x^2 + px + q = 0, if the roots are -2 and -3, what is the value

Practice Questions

Q1
For the equation x^2 + px + q = 0, if the roots are -2 and -3, what is the value of p?
  1. 5
  2. 6
  3. 7
  4. 8

Questions & Step-by-Step Solutions

For the equation x^2 + px + q = 0, if the roots are -2 and -3, what is the value of p?
  • Step 1: Identify the roots of the equation, which are given as -2 and -3.
  • Step 2: Use the formula for the sum of the roots of a quadratic equation, which is -p (where p is the coefficient of x).
  • Step 3: Calculate the sum of the roots: -2 + -3 = -5.
  • Step 4: Since the sum of the roots is -p, we have -p = -5.
  • Step 5: To find p, multiply both sides by -1: p = 5.
  • Quadratic Equations – Understanding the relationship between the coefficients and the roots of a quadratic equation.
  • Vieta's Formulas – Using Vieta's formulas to relate the sum and product of the roots to the coefficients of the polynomial.
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