Multiple choice

In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer I. 2x²-21x+54=0 II. y²-14y+49=0

  1. if x < y

  2. if x ≤ y

  3. if x = y or no relation can be established

  4. if x > y

  5. if x ≥ y
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

I: 2x^2 - 21x + 54 = 0. Roots are (21 +/- sqrt(441 - 432))/4 = (21 +/- 3)/4. Roots are 6 and 4.5. II: y^2 - 14y + 49 = 0. (y-7)^2 = 0. Root is 7. Comparing: 6 < 7 and 4.5 < 7, so x < y.

AI explanation

Factoring equation I, 2x squared minus 21x plus 54 equals 2x squared minus 12x minus 9x plus 54, which gives the roots x = 6 and x = 4.5. Factoring equation II, y squared minus 14y plus 49 equals (y - 7) squared = 0, giving the double root y = 7. Since the maximum value of x is 6 and the minimum value of y is 7, all values of x are smaller than y. Therefore, x < y.

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