I- x 2- x -6-0II- 2 y 2-13 y -21-0A- If x - yB- If x y

The correct option is E If x gt; yEquation I x^2 x 6=0 ⇒ x^2 3x+2x 6=0 ⇒ x(x 3)+2(x 3)=0 ⇒ (x+2)(x 3)=0 ⇒ x= 2 or 3 Equation II 2y^2+13y+21=0 ⇒ 2y^2+7y+6y+ ...

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Byju's Answer

Standard XII

Mathematics

Derivative of Standard Functions

I. x 2- x -6=...

Question

I. $x^{2} - x - 6 = 0$
II. $2 y^{2} + 13 y + 21 = 0$

x < y

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x \leq y

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x = y

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x \geq y

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x > y

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Solution

The correct option is E If $x > y$
Equation I
$x^{2} - x - 6 = 0$
$\Rightarrow x^{2} - 3 x + 2 x - 6 = 0$
$\Rightarrow x (x - 3) + 2 (x - 3) = 0$
$\Rightarrow (x + 2) (x - 3) = 0$
$\Rightarrow x = - 2$ or $3$

Equation II
$2 y^{2} + 13 y + 21 = 0$
$\Rightarrow 2 y^{2} + 7 y + 6 y + 21 = 0$
$\Rightarrow y (2 y + 7) + 3 (2 y + 7) = 0$
$\Rightarrow (y + 3) (2 y + 7) = 0$
$∴ y = - 3$ or $- \frac{7}{2}$
Hence, $x > y$

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I. x2−x−6=0 II. 2y2+13y+21=0

The correct option is E If x>yEquation I x2−x−6=0 ⇒x2−3x+2x−6=0 ⇒x(x−3)+2(x−3)=0 ⇒(x+2)(x−3)=0 ⇒x=−2 or 3 Equation II 2y2+13y+21=0 ⇒2y2+7y+6y+21=0 ⇒y(2y+7)+3(2y+7)=0 ⇒(y+3)(2y+7)=0 ∴y=−3 or −72 Hence, x>y

I. $x^{2} - x - 6 = 0$
II. $2 y^{2} + 13 y + 21 = 0$