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What is the value of k if the roots of the equation x^2 - kx + 12 = 0 are 3 and

Practice Questions

Q1
What is the value of k if the roots of the equation x^2 - kx + 12 = 0 are 3 and 4?
  1. 7
  2. 12
  3. 9
  4. 10

Questions & Step-by-Step Solutions

What is the value of k if the roots of the equation x^2 - kx + 12 = 0 are 3 and 4?
  • Step 1: Identify the given quadratic equation, which is x^2 - kx + 12 = 0.
  • Step 2: Recognize that the roots of the equation are given as 3 and 4.
  • 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, b = -k, and c = 12.
  • Step 5: Calculate the sum of the roots: 3 + 4 = 7.
  • Step 6: Set the sum of the roots equal to -(-k)/1, which simplifies to k.
  • Step 7: Therefore, we have k = 7.
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