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If the roots of the equation ax^2 + bx + c = 0 are equal, what is the condition

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Question: If the roots of the equation ax^2 + bx + c = 0 are equal, what is the condition on a, b, and c? (2020)

Options:

  1. b^2 - 4ac > 0
  2. b^2 - 4ac = 0
  3. b^2 - 4ac < 0
  4. a + b + c = 0

Correct Answer: b^2 - 4ac = 0

Exam Year: 2020

Solution: 

The condition for equal roots is given by the discriminant: b^2 - 4ac = 0.

If the roots of the equation ax^2 + bx + c = 0 are equal, what is the condition

Practice Questions

Q1
If the roots of the equation ax^2 + bx + c = 0 are equal, what is the condition on a, b, and c? (2020)
  1. b^2 - 4ac > 0
  2. b^2 - 4ac = 0
  3. b^2 - 4ac < 0
  4. a + b + c = 0

Questions & Step-by-Step Solutions

If the roots of the equation ax^2 + bx + c = 0 are equal, what is the condition on a, b, and c? (2020)
  • Step 1: Understand that the equation ax^2 + bx + c = 0 is a quadratic equation.
  • Step 2: Recognize that the roots of a quadratic equation can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).
  • Step 3: Identify that the term inside the square root, b² - 4ac, is called the discriminant.
  • Step 4: Know that if the roots are equal, the discriminant must be zero.
  • Step 5: Set up the condition for equal roots: b² - 4ac = 0.
  • Discriminant – The discriminant of a quadratic equation determines the nature of its roots; if it equals zero, the roots are equal.
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