Multiple choice

Directions: In the following question, two equations, labeled (I) and (II) are given. You have to solve both the equations and give answer. (I) 5x2 = 15 + 74x (II) 96y + 19 = -5y2

  1. x > y

  2. x < y

  3. x ≥ y

  4. x ≤ y

  5. x = y or there is no relation between 'x' and 'y'
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Eq I: 5x^2 - 74x - 15 = 0. Roots: x = (74 +/- sqrt(5476 + 300))/10 = (74 +/- 76)/10. x = 15 or -0.2. Eq II: 5y^2 + 96y + 19 = 0. Roots: y = (-96 +/- sqrt(9216 - 380))/10 = (-96 +/- 94)/10. y = -0.2 or -19. Comparing roots: x values are 15, -0.2; y values are -0.2, -19. Thus x >= y.

AI explanation

Rearranging equation one using the standard quadratic form gives 5x2 minus 74x minus 15 equals zero, which factors into (5x plus 1)(x minus 15) to yield x equals 15 or x equals minus 0.2. Rearranging the second equation similarly gives 5y2 plus 96y plus 19 equals zero, which factors into (5y plus 1)(y plus 19) to yield y equals minus 0.2 or y equals minus 19. Comparing all values, both roots of x are greater than or equal to the roots of y, so x is greater than or equal to y.

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