Multiple choice

Directions: In the given question, two equations (I) and (II) are given. You have to solve both the equations and select answer from the given options. I. 2x2 + 11x - 40 = 0 II. 4y2 - 27y + 44 = 0

  1. If x < y

  2. If x ≥ y

  3. If x > y

  4. If x ≤ y

  5. x = y, or the relationship cannot be established.
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A Correct answer
Explanation

I: 2x^2 + 11x - 40 = 0. Roots: x = (-11 +/- sqrt(121 + 320))/4 = (-11 +/- 21)/4. x = 2.5 or -8. II: 4y^2 - 27y + 44 = 0. Roots: y = (27 +/- sqrt(729 - 704))/8 = (27 +/- 5)/8. y = 4 or 2.75. Comparing values, x < y.

AI explanation

Factorizing equation one yields 2x^2 + 16x - 5x - 40 = 0, giving 2x(x + 8) - 5(x + 8) = 0, so x = -8 or 2.5. Factorizing equation two yields 4y^2 - 16y - 11y + 44 = 0, giving 4y(y - 4) - 11(y - 4) = 0, so y = 4 or 2.75. Comparing these values, both roots of x are smaller than both roots of y, therefore x < y.

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