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If the equation 2x^2 + 3x + k = 0 has one root equal to 1, what is the value of

Practice Questions

Q1
If the equation 2x^2 + 3x + k = 0 has one root equal to 1, what is the value of k?
  1. -1
  2. 0
  3. 1
  4. 2

Questions & Step-by-Step Solutions

If the equation 2x^2 + 3x + k = 0 has one root equal to 1, what is the value of k?
Correct Answer: -5
  • Step 1: Start with the equation 2x^2 + 3x + k = 0.
  • Step 2: We know one root of the equation is x = 1.
  • Step 3: Substitute x = 1 into the equation: 2(1)^2 + 3(1) + k = 0.
  • Step 4: Calculate (1)^2, which is 1, so we have 2(1) + 3(1) + k = 0.
  • Step 5: This simplifies to 2 + 3 + k = 0.
  • Step 6: Add 2 and 3 together to get 5, so we have 5 + k = 0.
  • Step 7: To find k, subtract 5 from both sides: k = -5.
  • Quadratic Equations – Understanding how to manipulate and solve quadratic equations, particularly when given specific conditions about the roots.
  • Substitution – Applying substitution of a known root into the equation to find unknown coefficients.
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