The set of solutions satisfying both x 2-5 x -6 - 0 and x 2-3 x -4-0 isA- -4-1- -4-3 -2-1- -4-3- -2-1D- -4-3- -2-1-

The correct option is nbsp;C nbsp; nbsp;(( 4, 3]∪ [ 2,1))Given inequalities x^2+5x+6≥ 0 and x^2+3x 4 lt;0⇒ x^2+3x+2x+6≥ 0 and x^2+4x x 4 lt;0⇒ x(x+3)+ ...

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Standard XII

Mathematics

Relation between Roots and Coefficients for Quadratic

The set of so...

Question

The set of solutions satisfying both $x^{2} + 5 x + 6 \geq 0 a n d x^{2} + 3 x - 4 < 0 i s$

$(- 4, 1)$

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$(- 4, - 3] \cup [- 2, 1)$

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$(- 4, - 3) \cup (- 2, 1)$

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$[- 4, - 3] \cup [- 2, 1]$

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Solution

The correct option is C $((- 4, - 3] \cup [- 2, 1))$
Given inequalities $x^{2} + 5 x + 6 \geq 0$ and $x^{2} + 3 x - 4 < 0$
$\Rightarrow x^{2} + 3 x + 2 x + 6 \geq 0$ and $x^{2} + 4 x - x - 4 < 0$
$\Rightarrow x (x + 3) + 2 (x + 3) \geq 0$ and $x (x + 4) - 1 (x + 4) < 0$
$\Rightarrow (x + 3) (x + 2) \geq 0$ and $(x + 4) (x - 1) < 0$
$\Rightarrow x \leq - 3 o r x \geq - 2$ and $- 4 < x < 1$
$∴ x ϵ (- 4, - 3] \cup [- 2, 1)$

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Similar questions

Q. The set of solutions satisfying both

x^{2} + 5 x + 6 \geq 0

and

x^{2} + 3 x - 4 < 0

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Q. Match the elements of the list I, which contains inequalities, with the elements of list II, which has solution sets.

List-I (Inequality)	List-II (Solution set)
A) $x^{2} - 4 x + 3 > 0$	1) $(3, 4)$
B) $x^{2} - 5 x + 6 \leq 0$	2) $(- 1, 1) \cup (2, 4)$
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Then the correct order for A B C D, is

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Q. By graphical method, the solution of linear programming problem

Maximize Z = 3 x_{1} + 5 x_{2} Subject to 3 x_{1} + 2 x_{2} \leq 18 x_{1} \leq 4 x_{2} \leq 6 x_{1} \geq 0, x_{2} \geq 0, is

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The set of solutions satisfying both x2+5x+6≥0 and x2+3x−4<0 is

The correct option is C ((−4,−3]∪[−2,1))Given inequalities x2+5x+6≥0 and x2+3x−4<0⇒x2+3x+2x+6≥0 and x2+4x−x−4<0⇒x(x+3)+2(x+3)≥0 and x(x+4)−1(x+4)<0⇒(x+3)(x+2)≥0 and (x+4)(x−1)<0⇒x≤−3 or x≥−2and −4<x<1 ∴x ϵ(−4,−3]∪[−2,1)

The set of solutions satisfying both $x^{2} + 5 x + 6 \geq 0 a n d x^{2} + 3 x - 4 < 0 i s$