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If the roots of the equation x² + 7x + k = 0 are 1 and 6, what is the value of k

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Question: If the roots of the equation x² + 7x + k = 0 are 1 and 6, what is the value of k? (2020)

Options:

  1. 6
  2. 7
  3. 8
  4. 9

Correct Answer: 8

Exam Year: 2020

Solution: 

Using the product of roots, k = 1*6 = 6.

If the roots of the equation x² + 7x + k = 0 are 1 and 6, what is the value of k

Practice Questions

Q1
If the roots of the equation x² + 7x + k = 0 are 1 and 6, what is the value of k? (2020)
  1. 6
  2. 7
  3. 8
  4. 9

Questions & Step-by-Step Solutions

If the roots of the equation x² + 7x + k = 0 are 1 and 6, what is the value of k? (2020)
  • Step 1: Identify the equation given, which is x² + 7x + k = 0.
  • Step 2: Recognize that the roots of the equation are given as 1 and 6.
  • Step 3: Use the property of quadratic equations that states the product of the roots (r1 * r2) is equal to k.
  • Step 4: Calculate the product of the roots: 1 * 6 = 6.
  • Step 5: Conclude that the value of k is 6.
  • 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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