Multiple choice

Which of the following equations has imaginary roots?

  1. 5x2 + 2x + 4 = 0

  2. x2 - 8x + 16 = 0

  3. x2 - 11x + 2 = 0

  4. None of these
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A Correct answer
Explanation

A quadratic equation has imaginary roots if the discriminant D = b^2 - 4ac < 0. For 5x^2 + 2x + 4 = 0, D = 4 - 4(5)(4) = 4 - 80 = -76.

AI explanation

A quadratic equation ax^2 + bx + c = 0 has imaginary roots if its discriminant, b^2 - 4ac, is strictly less than zero. For the equation 5x^2 + 2x + 4 = 0, the discriminant is 2^2 - 4(5)(4), which equals 4 - 80 = -76. Because -76 is less than zero, this equation has imaginary roots.

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