Multiple choice

Directions: Equations I and II are given. You have to solve both the equations and choose the correct answer. I. 10x2 = 4 - 6x II. 3y2 + 7y + 4 = 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

Eq I: 10x^2 + 6x - 4 = 0 -> 5x^2 + 3x - 2 = 0 -> (5x-2)(x+1) = 0. x = 0.4 or -1. Eq II: 3y^2 + 7y + 4 = 0 -> (3y+4)(y+1) = 0. y = -4/3 or -1. Comparing values, x >= y.

AI explanation

Rearranging the first equation gives 10x2 plus 6x minus 4 equals zero, which factors into (5x minus 2)(2x plus 2) equals zero to yield x equals 0.4 or x equals minus 1. Factoring the second equation, 3y2 plus 7y plus 4 equals zero, yields (3y plus 4)(y plus 1) equals zero, resulting in the roots y equals minus 1 and y equals minus 4 divided by 3. Since the smallest root for x is minus 1 and the largest root for y is minus 1, all corresponding values of x are greater than or equal to the values of y. Therefore, x is greater than or equal to y.

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