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If the roots of the equation x² + 5x + q = 0 are 1 and 4, find q. (2019)

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Question: If the roots of the equation x² + 5x + q = 0 are 1 and 4, find q. (2019)

Options:

  1. 5
  2. 4
  3. 6
  4. 7

Correct Answer: 5

Exam Year: 2019

Solution: 

Using the product of roots: q = 1 * 4 = 4.

If the roots of the equation x² + 5x + q = 0 are 1 and 4, find q. (2019)

Practice Questions

Q1
If the roots of the equation x² + 5x + q = 0 are 1 and 4, find q. (2019)
  1. 5
  2. 4
  3. 6
  4. 7

Questions & Step-by-Step Solutions

If the roots of the equation x² + 5x + q = 0 are 1 and 4, find q. (2019)
  • Step 1: Identify the equation given, which is x² + 5x + q = 0.
  • Step 2: Recognize that the roots of the equation are given as 1 and 4.
  • Step 3: Use the property of quadratic equations that states the product of the roots (r1 * r2) is equal to q.
  • Step 4: Calculate the product of the roots: 1 * 4.
  • Step 5: Find the result of the multiplication: 1 * 4 = 4.
  • Step 6: Conclude that q = 4.
  • 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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