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If the roots of the equation x^2 + 5x + c = 0 are 2 and 3, what is the value of

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Question: If the roots of the equation x^2 + 5x + c = 0 are 2 and 3, what is the value of c? (2022)

Options:

  1. 6
  2. 5
  3. 7
  4. 8

Correct Answer: 6

Exam Year: 2022

Solution: 

Using the product of the roots, c = 2 * 3 = 6.

If the roots of the equation x^2 + 5x + c = 0 are 2 and 3, what is the value of

Practice Questions

Q1
If the roots of the equation x^2 + 5x + c = 0 are 2 and 3, what is the value of c? (2022)
  1. 6
  2. 5
  3. 7
  4. 8

Questions & Step-by-Step Solutions

If the roots of the equation x^2 + 5x + c = 0 are 2 and 3, what is the value of c? (2022)
  • Step 1: Identify the equation given, which is x^2 + 5x + c = 0.
  • Step 2: Recognize that the roots of the equation are given as 2 and 3.
  • Step 3: Recall that for a quadratic equation ax^2 + bx + c = 0, the product of the roots (r1 and r2) can be found using the formula r1 * r2 = c.
  • Step 4: Calculate the product of the roots: 2 * 3.
  • Step 5: Perform the multiplication: 2 * 3 = 6.
  • Step 6: Conclude that the value of c 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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