Multiple choice

The nature of the roots of the equation √3 x2 −2√2 x−2√3=0 i s

  1. none of these

  2. not real

  3. real and equal

  4. real and unequal
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Discriminant D = b^2 - 4ac = (-2*sqrt(2))^2 - 4*(sqrt(3))(-2*sqrt(3)) = 8 - 4(-6) = 8 + 24 = 32. Since D > 0, roots are real and unequal.

AI explanation

The discriminant determines the nature of the roots using the formula D = b^2 - 4ac. Substituting a = the square root of 3, b = negative 2 times the square root of 2, and c = negative 2 times the square root of 3 gives 8 minus 4 times the square root of 3 times negative 2 times the square root of 3, which simplifies to 8 plus 24. Because the discriminant is 32, which is greater than zero, the roots are real and unequal.

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