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If the roots of the equation x^2 + px + q = 0 are 4 and -2, what is the value of

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Question: If the roots of the equation x^2 + px + q = 0 are 4 and -2, what is the value of p?

Options:

  1. 2
  2. 6
  3. -2
  4. -6

Correct Answer: 2

Solution: 

Using the sum of roots formula, p = -(4 + (-2)) = -2.

If the roots of the equation x^2 + px + q = 0 are 4 and -2, what is the value of

Practice Questions

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

Questions & Step-by-Step Solutions

If the roots of the equation x^2 + px + q = 0 are 4 and -2, what is the value of p?
  • Step 1: Identify the roots of the equation. The roots given are 4 and -2.
  • Step 2: Recall the formula for the sum of the roots of a quadratic equation ax^2 + bx + c = 0, which is -b/a.
  • Step 3: In our equation, a = 1 (since it's x^2), b = p, and c = q.
  • Step 4: Calculate the sum of the roots: 4 + (-2) = 4 - 2 = 2.
  • Step 5: Set the sum of the roots equal to -b/a. Since a = 1, we have: 2 = -p.
  • Step 6: Solve for p: p = -2.
  • Sum of Roots – The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is given by -b/a.
  • Quadratic Equation – A quadratic equation is a polynomial equation of degree 2, typically in the form x^2 + px + q = 0.
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