In the following question, two equations numbered I and II are given. Solve both the equations and mark the appropriate option:

I. $32 x^{2} - 68 x + 35 = 0$
II. $y^{2} + 10 y + 24 = 0$

if x > y

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if x < y

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if x

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if x

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if x = y or relationship between x and y cannot be determined

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Solution

The correct option is A if x > y
$32 x^{2} - 68 x + 35 = 0 \Rightarrow (4 x - 5) (8 x - 7) = 0 \Rightarrow x = \frac{5}{4}, \frac{7}{8} \Rightarrow y^{2} + 10 y + 24 = 0 \Rightarrow (y + 4) (y + 6) = 0 \Rightarrow y = - 4, - 6 ∴ x > y$

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