Multiple choice

Determine the nature of the roots of the equation: $x^2-8x+12=0$

  1. Real and unequal

  2. Real and equal

  3. Imaginary

  4. None of these
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A Correct answer
Explanation

For x^2 - 8x + 12 = 0, the discriminant D = b^2 - 4ac = (-8)^2 - 4(1)(12) = 64 - 48 = 16. Since D > 0 and is a perfect square, the roots are real, rational, and unequal.

AI explanation

The nature of the roots is determined by the discriminant, which is calculated as D = b^2 - 4ac. For the equation x^2 - 8x + 12 = 0, the discriminant is (-8)^2 - 4(1)(12) = 64 - 48 = 16. Since 16 is a positive number, the equation has real and unequal roots.

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