In the following question, two equations numbered I and II are given. Solve both the equations and mark the appropriate option:
I. $x^{2} + 5 x + 6 = 0$
II. $y^{2} + 7 y + 12 = 0$

if x

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if x > y

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if x

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if x < y

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if x = y, or no definite relationship can be established between x and y

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Solution

The correct option is A if x y
$I . x^{2} + 5 x + 6 = 0 \Rightarrow x^{2} + 2 x + 3 x + 6 = 0 \Rightarrow x (x + 2) + 3 (x + 2) = 0 \Rightarrow (x + 3) (x + 2) = 0 ∴ x = - 3 o r - 2$

$I I . y^{2} + 7 y + 12 = 0 \Rightarrow y^{2} + 4 y + 3 y + 12 = 0 \Rightarrow y (y + 4) + 3 (y + 4) = 0 \Rightarrow (y + 3) (y + 4) = 0 ∴ y = - 3 o r - 4$

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In the following question, two equations numbered I and II are given. Solve both the equations and mark the appropriate option: I. x2+5x+6=0 II. y2+7y+12=0

The correct option is A if x yI. x2+5x+6=0⇒x2+2x+3x+6=0⇒x(x+2)+3(x+2)=0⇒(x+3)(x+2)=0∴ x=−3 or −2 II.y2+7y+12=0⇒y2+4y+3y+12=0⇒y(y+4)+3(y+4)=0⇒(y+3)(y+4)=0∴ y=−3 or −4

In the following question, two equations numbered I and II are given. Solve both the equations and mark the appropriate option:
I. $x^{2} + 5 x + 6 = 0$
II. $y^{2} + 7 y + 12 = 0$