If A=x∈R/(x^2)+5x+6=0 then nA=

Correct answer: (A) 0. We have, A=x∈R/(x^2)+5x+6=0 Now, x^2+5x+6=0 …i ⇒x^2+3x+2x+6=0 ⇒xx+3+2x+3=0 ⇒x+2x+3=0 ⇒x=-2x=-3 ⇒x≠2 or x≠3 Here, no value of x satisfy the Eq. (i). ∴nA=0

Q89 / 150 · MHT CET 2019 (Shift 1) · Mathematics

If $A = \{x \in \frac{R}{x^{2}} + 5 |x| + 6 = 0\}$ then $n (A) =$

Correct answer
A
0
B
4
C
1
D
2

Solution

We have,

A = \{x \in \frac{R}{x^{2}} + 5 |x| + 6 = 0\}

Now,

x^{2} + 5 |x| + 6 = 0 \dots (i)

\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 |x| = - 3

\Rightarrow x \neq 2 o r x \neq 3

Here, no value of x satisfy the Eq. (i).

∴ n (A) = 0

Hence, the correct answer is option: 'A'.

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If A=x∈Rx2+5x+6=0 then nA=

Solution

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If $A = \{x \in \frac{R}{x^{2}} + 5 |x| + 6 = 0\}$ then $n (A) =$