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. 12x²-17x+6=0 II. y²-16y+63=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

For 12x^2 - 17x + 6 = 0, the roots are x = 2/3 and x = 3/4. For y^2 - 16y + 63 = 0, the roots are y = 7 and y = 9. Since both roots of x are smaller than both roots of y, x < y.

AI explanation

Factoring equation I, 12x squared minus 17x plus 6 equals 12x squared minus 9x minus 8x plus 6, which gives the roots x = 3/4 and x = 2/3. Factoring equation II, y squared minus 16y plus 63 equals (y - 7)(y - 9) = 0, giving the roots y = 7 and y = 9. Since the maximum value of x is 0.75 and the minimum value of y is 7, all values of x are smaller than all values of y. Therefore, x < y.

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