Multiple choice

Which of the following equations has real and distinct roots?

  1. x2 - 5x + 5 = 0

  2. 2x2 - 12x + 2 = 0

  3. 2x2 + 5x + 1 = 0

  4. All of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A quadratic equation has real and distinct roots if the discriminant D = b^2 - 4ac > 0. For A: 25 - 20 = 5 > 0. For B: 144 - 16 = 128 > 0. For C: 25 - 8 = 17 > 0. All satisfy the condition.

AI explanation

For a quadratic equation to have real and distinct roots, its discriminant (b2 - 4ac) must be greater than zero. For x2 - 5x + 5 = 0, the discriminant is 25 - 20 = 5; for 2x2 - 12x + 2 = 0, it is 144 - 16 = 128; for 2x2 + 5x + 1 = 0, it is 25 - 8 = 17. Since the discriminant is positive for all three equations, they all have real and distinct roots. The result is all of the above.

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