Directions (49-53): In these questions, two equations numbered I and II are given.
You have to solve both the equations and
Give answer:
(1) If X > y
(2) If x ≥ y
(3) x < y
(4) If relationship between x and y cannot be determined
(5) If x ≤ y
I. \( \Large 6x^{2} + 25x + 24 = 0 \)
II.\( \Large 12y^{2} + 13y + 3 =0 \)
Correct Answer: Description for Correct answer:
I. \( \Large 6x^{2} + 25x + 24 = 0 \)
\( \Large 6x^{2} + 16x + 9x + 24 = 0 \)
\( \Large 2x \left(3x + 8\right) + 3 \left(3x + 8\right) = 0 \)
\( \Large \left(2x + 3\right) \left(3x + 8\right) = 0 \)
\( \Large x = \frac{-3}{2}, \frac{-8}{3} \)
II. \( \Large 12y^{2} + 13y + 3 = 0\)
\( \Large 12y^{2} + 9y + 4y + 3 = 0\)
\( \Large 3y \left(4y + 3\right) + 1 \left(4y + 3\right) = 0 \)
\( \Large \left(3y + 1\right) \left(4y + 3\right) = 0 \)
\( \Large y = \frac{-1}{3}, \frac{-3}{4} \)
Hence, y > x
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