Multiple choice

If the roots of the equation $2x^2-3x + c = 0$ are real and irrational, a possible value of c is

  1. -2

  2. -1

  3. 0

  4. 1

  5. 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For roots to be real and irrational, the discriminant D = b^2 - 4ac must be a positive non-perfect square. Here, D = (-3)^2 - 4(2)(c) = 9 - 8c. For D > 0, 9 - 8c > 0, so c < 9/8. Checking options: if c = -1, D = 9 - 8(-1) = 17, which is positive and not a perfect square, making the roots irrational.

AI explanation

The discriminant of the quadratic equation 2x^2 - 3x + c = 0 is D = (-3)^2 - 4(2)(c), which simplifies to 9 - 8c. For the roots to be real and irrational, the discriminant must be positive and not a perfect square. Substituting c = -1 gives D = 9 - 8(-1) = 17, which is a positive non-square integer. Therefore, c = -1 provides real and irrational roots.

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