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If the roots of the equation ax^2 + bx + c = 0 are 3 and -2, what is the value o

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Question: If the roots of the equation ax^2 + bx + c = 0 are 3 and -2, what is the value of b if a = 1 and c = -6?

Options:

  1. -1
  2. 1
  3. 5
  4. -5

Correct Answer: -1

Solution: 

Using the sum of roots (-b/a = 3 + (-2) = 1), we find b = -1.

If the roots of the equation ax^2 + bx + c = 0 are 3 and -2, what is the value o

Practice Questions

Q1
If the roots of the equation ax^2 + bx + c = 0 are 3 and -2, what is the value of b if a = 1 and c = -6?
  1. -1
  2. 1
  3. 5
  4. -5

Questions & Step-by-Step Solutions

If the roots of the equation ax^2 + bx + c = 0 are 3 and -2, what is the value of b if a = 1 and c = -6?
  • Step 1: Identify the given equation format, which is ax^2 + bx + c = 0.
  • Step 2: Note that the roots of the equation are given as 3 and -2.
  • Step 3: Recall the formula for the sum of the roots, which is -b/a.
  • Step 4: Substitute the values of the roots into the sum formula: 3 + (-2) = 1.
  • Step 5: Set up the equation: -b/a = 1. Since a = 1, this simplifies to -b = 1.
  • Step 6: Solve for b by multiplying both sides by -1: b = -1.
  • Quadratic Equations – Understanding the relationship between the coefficients and the roots of a quadratic equation.
  • Sum and Product of Roots – Using the formulas for the sum and product of the roots to find coefficients in a quadratic equation.
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