# In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer. I. 3x2 + 16x + 21 = 0 II.

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In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.

I. 3x2 + 16x + 21 = 0

II. 6y2 + 17y + 12 = 0

1. x > y
2. x < y
3. x ≥ y
4. x ≤ y
5. No relation in x and y or x = y

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Correct Answer - Option 2 : x < y

Calculation:

From I,

3x2 + 16x + 21 = 0

⇒ 3x2 + 9x + 7x + 21 = 0

⇒ 3x(x + 3) + 7(x + 3) = 0

⇒ (x + 3)(3x + 7) = 0

Taking,

⇒ x + 3 = 0 or 3x + 7 = 0

⇒ x = – 3 or x = – 7/3

From II,

6y2 + 17y + 12 = 0

⇒ 6y2 + 9y + 8y + 12 = 0

⇒ 3y(2y + 3) + 4(2y + 3) = 0

⇒ (3y + 4)(2y + 3) = 0

Taking,

⇒ 2y + 3 = 0 or 3y + 4 = 0

⇒ y = – 3/2 or y = – 4/3

Comparison between x and y (via Tabulation):

 x Y Relation – 3 – 3/2 x < y – 3 – 4/3 x < y – 7/3 – 3/2 x < y – 7/3 – 4/3 x < y

∴ After comparing x and y both, x < y.