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

The correct option is A If x lt; yEquation I x^2+x 6=0 ⇒ x^2+3x 2x 6=0 ⇒ x(x+3) 2(x+3)=0 ⇒ (x+3)(x 2)=0 ⇒ x= 3 or 2 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 A If $x < y$
Equation I
$x^{2} + x - 6 = 0$
$\Rightarrow x^{2} + 3 x - 2 x - 6 = 0$
$\Rightarrow x (x + 3) - 2 (x + 3) = 0$
$\Rightarrow (x + 3) (x - 2) = 0$
$\Rightarrow x = - 3$ or $2$

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

Suggest Corrections

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I. x2+x−6=0 II. 2y2−13y+21=0

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

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