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For the quadratic equation x^2 + px + q = 0, if the roots are 1 and -3, what is

Practice Questions

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

Questions & Step-by-Step Solutions

For the quadratic equation x^2 + px + q = 0, if the roots are 1 and -3, what is the value of p?
  • Step 1: Identify the roots of the quadratic equation, which are given as 1 and -3.
  • Step 2: Calculate the sum of the roots by adding them together: 1 + (-3).
  • Step 3: Simplify the sum: 1 - 3 = -2.
  • Step 4: In a quadratic equation of the form x^2 + px + q = 0, the sum of the roots is equal to -p.
  • Step 5: Since we found the sum of the roots to be -2, we can set -p = -2.
  • Step 6: To find p, multiply both sides of the equation by -1: p = 2.
  • 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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