Register

CAT 2019 Set-1 | Question: 99

• edited by
588 views

1 Answer

1 votes
1 votes
Given that, $ \left | x \right | (6x^{2}+1) = 5x^{2} $

We know that, $\left | x \right | = \left\{\begin{matrix} x\; ;& x \geq 0 \\  -x \; ;& x<0 \end{matrix}\right.$

$\textbf{Case 1:} \; x \geq 0 $

 Now, $x (6x^{2} + 1) = 5x^{2} $

$ \Rightarrow 6x^{3} + x = 5x^{2} $

$ \Rightarrow 6x^{3} – 5x^{2} + x = 0 $

$ \Rightarrow x( 6x^{2} -5x +1) = 0$

$ \Rightarrow x ( 6x^{2} -3x – 2x +1) = 0 $

$ \Rightarrow x [3x (2x-1) -1(2x-1)] = 0 $

$ \Rightarrow x [ (3x-1)(2x-1)] = 0 $

$ \Rightarrow x=0 , (3x-1)=0 , (2x-1)=0 $

$ \boxed{x=0,x=\frac{1}{3},x=\frac{1}{2}} $

$\therefore$ The number of solutions $=3$

$\textbf{Case 2:}\; x < 0$

Now, $ -x(6x^{2}+1) = 5x^{2} $

$ \Rightarrow – 6x^{3} – x – 5x^{2} = 0 $

$\Rightarrow 6x^{3} + 5x^{2} + x = 0 $

$ \Rightarrow x (6x^{2} + 5x + 1) = 0 $

$\Rightarrow x (6x^{2} + 3x + 2x + 1) = 0 $

$ \Rightarrow x [3x(2x+1) +1(2x+1)] = 0$

$ \Rightarrow x [(3x+1)(2x+1)] = 0 $

$\Rightarrow x=0,(3x+1)=0,(2x+1)=0 $

$ \boxed {x=0,x=\frac{-1}{3},x=\frac{-1}{2}} $

$\therefore$ The number of solutions $=3$

So, the total number of solutions $ = 2 + 3 = 5.$

Correct Answer $:5$
• edited by
User Avatar
Voting & Accepting an answer helps improve the community
← PreviousNext →
← Previous in categoryNext in category →
Answer:

Related questions

2 votes
2 votes
1 answer
1
go_editor asked Mar 8, 2020
596 views
CAT 2019 Set-1 | Question: 72
Let $\text{S}$ be the set of all points $(x,y)$ in the $x-y$ plane such that $|x|+|y|\leq 2$ and $|x|\geq 1$. Then, the area, in square units, of the region represented by $\text{S}$ equals ________
Let $\text{S}$ be the set of all points $(x,y)$ in the $x-y$ plane such that $|x|+|y|\leq 2$ and $|x|\geq 1$. Then, the area, in square units, of the region represented b...
2 votes
2 votes
1 answer
2
go_editor asked Mar 8, 2020
645 views
CAT 2019 Set-1 | Question: 84
The product of the distinct roots of $|x^{2}-x-6|=x+2$ is $-8$ $-24$ $-4$ $-16$
The product of the distinct roots of $|x^{2}-x-6|=x+2$ is$-8$$-24$$-4$$-16$
1 votes
1 votes
1 answer
3
go_editor asked Mar 8, 2020
666 views
CAT 2019 Set-1 | Question: 69
In a class, $60\%$ of the students are girls and the rest are boys. There are $30$ more girls than boys. If $68\%$ of the students, including $30$ boys, pass an examination, the percentage of the girls who do not pass is _______
In a class, $60\%$ of the students are girls and the rest are boys. There are $30$ more girls than boys. If $68\%$ of the students, including $30$ boys, pass an examinati...
2 votes
2 votes
1 answer
4
go_editor asked Mar 8, 2020
616 views
CAT 2019 Set-1 | Question: 77
With rectangular axes of coordinates, the number of paths from $(1,1)$ to $(8,10)$ via $(4,6)$, where each step from any point $(x,y)$ is either to $(x,y+1)$ or to $(x+1, y)$, is _______
With rectangular axes of coordinates, the number of paths from $(1,1)$ to $(8,10)$ via $(4,6)$, where each step from any point $(x,y)$ is either to $(x,y+1)$ or to $(x+1,...
2 votes
2 votes
1 answer
5
go_editor asked Mar 8, 2020
534 views
CAT 2019 Set-1 | Question: 80
Let T be the triangle formed by the straight line $3x+5y-45=0$ and T the coordinate axes. Let the circumcircle of T have radius of length L, measured in the same unit as the coordinate axes. Then, the integer closest to L is ______
Let T be the triangle formed by the straight line $3x+5y-45=0$ and T the coordinate axes. Let the circumcircle of T have radius of length L, measured in the same unit as ...
Link Copied!