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If the roots of the equation x² + 7x + p = 0 are -3 and -4, what is the value of

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Question: If the roots of the equation x² + 7x + p = 0 are -3 and -4, what is the value of p? (2019)

Options:

  1. 12
  2. 7
  3. 15
  4. 10

Correct Answer: 12

Exam Year: 2019

Solution: 

Using the product of roots: p = (-3)(-4) = 12.

If the roots of the equation x² + 7x + p = 0 are -3 and -4, what is the value of

Practice Questions

Q1
If the roots of the equation x² + 7x + p = 0 are -3 and -4, what is the value of p? (2019)
  1. 12
  2. 7
  3. 15
  4. 10

Questions & Step-by-Step Solutions

If the roots of the equation x² + 7x + p = 0 are -3 and -4, what is the value of p? (2019)
  • Step 1: Identify the given quadratic equation, which is x² + 7x + p = 0.
  • Step 2: Recognize that the roots of the equation are given as -3 and -4.
  • Step 3: Recall the property of quadratic equations that states the product of the roots (r1 and r2) is equal to p.
  • Step 4: Calculate the product of the roots: Multiply -3 and -4.
  • Step 5: Perform the multiplication: -3 * -4 = 12.
  • Step 6: Conclude that the value of p is 12.
  • 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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