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. 76x2 + 29√19x + 52 = 0 II. 35y2 + 8y – 3 = 0

  1. if x > y

  2. if x ≤ y

  3. if x ≥ y

  4. if x < y

  5. if x = y or relationship between x and y can't be established
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Solving 76x^2 + 29*sqrt(19)x + 52 = 0: roots are negative. Solving 35y^2 + 8y - 3 = 0: (5y-1)(7y+3)=0, y = 1/5 or -3/7. Since x is negative and y can be positive, x < y.

AI explanation

Solving equation I, the roots are found by factoring 76x squared plus 29 times the square root of 19 times x plus 52 equals 0 as (4x plus the square root of 19)(19x plus 4 times the square root of 19) equals 0, giving negative roots of roughly -1.09 and -0.91. Solving equation II, 35y squared plus 8y minus 3 equals 0 factors to (7y minus 1)(5y plus 3) equals 0, giving y equals 1 over 7 and y equals negative 3 over 5. Comparing the values, the largest x value is about -0.91, which is less than the smallest y value of -0.6, so x is less than y.

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