Multiple choice

Directions: In this question, two equations numbered I and II are given. You have to solve both the equations and mark the correct answer. (I) 14x2 - 51x = -7 (II) 1 - 6y - 7y2 = 0

  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
C Correct answer
Explanation

I: 14x^2 - 51x + 7 = 0. Roots are (51 +/- sqrt(2601 - 392))/28 = (51 +/- 47)/28. x = 98/28 = 3.5 or 4/28 = 1/7. II: 7y^2 + 6y - 1 = 0. (7y-1)(y+1) = 0. y = 1/7 or -1. Comparing x and y, x >= y.

AI explanation

Rearranging the first equation yields 14x2 - 51x + 7 = 0, and factoring gives (2x - 7)(7x - 1) = 0 for roots x = 7/2 and x = 1/7. Factoring the second equation gives (y - 1)(1 + 7y) = 0 for roots y = 1 and y = -1/7. When comparing the roots, both 7/2 and 1/7 are strictly greater than both 1 and -1/7. Therefore, x is always greater than y, meaning x is greater than or equal to y.

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