Multiple choice

Directions: Equation I and II are given. You have to solve both the equations and find out the relation, if any between x and y. I. 2x2 + 73x + 71 = 0 II. 11y + 6 = 21y2

  1. x > y

  2. x < y

  3. x ≥ y

  4. x ≤ y

  5. x = y or no relationship can be established between 'x' and 'y'.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

I: 2x^2 + 73x + 71 = 0. (2x + 71)(x + 1) = 0. Roots are x = -1, x = -35.5. II: 21y^2 - 11y - 6 = 0. (7y + 2)(3y - 3) is wrong. Using quadratic formula: y = (11 +/- sqrt(121 - 4*21*(-6))) / 42 = (11 +/- sqrt(121 + 504)) / 42 = (11 +/- 25) / 42. y = 36/42 = 6/7 or y = -14/42 = -1/3. Comparing roots: x = -1, -35.5 and y = 0.85, -0.33. In all cases, x < y.

AI explanation

Equation I factors to (2x + 71)(x + 1) = 0, yielding x = -35.5 and x = -1. Equation II can be rewritten as 21y2 - 11y - 6 = 0, which factors to (3y - 2)(7y + 3) = 0, giving y = 2/3 and y = -3/7. Because both roots of x are less than both roots of y, x < y.

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