Multiple choice

Determine the nature of roots of the given equation from its discriminant. $x^{2}\, +\, 3\sqrt2x\, -\, 8\, =\, 0$

  1. Real and unequal

  2. Real and equal

  3. One real and one imaginary

  4. Both imaginary
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A Correct answer
Explanation

Discriminant D = b^2 - 4ac. Here a=1, b=3*sqrt(2), c=-8. D = (3*sqrt(2))^2 - 4(1)(-8) = (9*2) + 32 = 18 + 32 = 50. Since D > 0, the roots are real and unequal.

AI explanation

Calculate the discriminant using D equals b squared minus 4ac. For the equation x squared plus 3 times the square root of 2 times x minus 8 equals 0, D equals (3 times the square root of 2) squared minus 4 times 1 times -8, which simplifies to 18 plus 32, or 50. Since 50 is greater than zero, the roots are real and unequal.

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