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If the roots of the quadratic equation ax^2 + bx + c = 0 are 4 and -1, what is t

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Question: If the roots of the quadratic equation ax^2 + bx + c = 0 are 4 and -1, what is the value of b if a = 1 and c = -4? (2023)

Options:

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

Correct Answer: -3

Exam Year: 2023

Solution: 

Using the sum of roots, b = - (4 + (-1)) = -3.

If the roots of the quadratic equation ax^2 + bx + c = 0 are 4 and -1, what is t

Practice Questions

Q1
If the roots of the quadratic equation ax^2 + bx + c = 0 are 4 and -1, what is the value of b if a = 1 and c = -4? (2023)
  1. -3
  2. 3
  3. 5
  4. -5

Questions & Step-by-Step Solutions

If the roots of the quadratic equation ax^2 + bx + c = 0 are 4 and -1, what is the value of b if a = 1 and c = -4? (2023)
  • Step 1: Identify the roots of the quadratic equation, which are given as 4 and -1.
  • Step 2: Use the formula for the sum of the roots of a quadratic equation, which is -b/a.
  • Step 3: Since a = 1, the formula simplifies to -b = sum of the roots.
  • Step 4: Calculate the sum of the roots: 4 + (-1) = 4 - 1 = 3.
  • Step 5: Substitute the sum into the equation: -b = 3.
  • Step 6: To find b, multiply both sides by -1: b = -3.
  • Roots of Quadratic Equations – Understanding how to find the coefficients of a quadratic equation using its roots.
  • Sum and Product of Roots – Applying the relationships between the coefficients and the roots of a quadratic equation.
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