Which of the following equations does not have real roots?
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x2 + x - 5 = 0
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5x2 - 3x + 1 = 0
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-x2 + 2x + 3 = 0
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x2 + 3x - 12 = 0
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7x2 - x - 12 = 0
Reveal answer
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B
Correct answer
Explanation
A quadratic equation ax^2 + bx + c = 0 has no real roots if the discriminant D = b^2 - 4ac < 0. For B: 5x^2 - 3x + 1 = 0, D = (-3)^2 - 4(5)(1) = 9 - 20 = -11. Since D < 0, it has no real roots.
AI explanation
A quadratic equation ax^2 + bx + c = 0 does not have real roots if its discriminant, b^2 - 4ac, is less than zero. For the equation 5x^2 - 3x + 1 = 0, the discriminant is (-3)^2 - 4(5)(1) = 9 - 20 = -11. Since the discriminant is negative, this equation does not have real roots.