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If the roots of the equation x^2 + px + q = 0 are 1 and -1, what is the value of

Practice Questions

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

Questions & Step-by-Step Solutions

If the roots of the equation x^2 + px + q = 0 are 1 and -1, what is the value of p?
Correct Answer: 0
  • Step 1: Identify the roots of the equation. The roots given are 1 and -1.
  • Step 2: Use the formula for the sum of the roots of a quadratic equation, which is -p. The sum of the roots (1 + (-1)) is 0.
  • Step 3: Set up the equation based on the sum of the roots: -p = 0.
  • Step 4: Solve for p. If -p = 0, then p must be 0.
  • Roots of Quadratic Equations – Understanding how to find the coefficients of a quadratic equation using its roots.
  • Sum and Product of Roots – Applying Vieta's formulas, which relate the coefficients of a polynomial to sums and products of its roots.
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