Answer
Verified
480k+ views
Hint: : The first step is to simplify the given equation by taking the mod value and equating it to a variable, then to find the roots we will factorise the simplified equation and then we will find the roots.
Given equation is $|x - 3{|^2} + |x - 3| - 2 = 0$
To simplify the equation, let us consider $|x - 3| = a$,
${a^2} + a - 2 = 0$
Therefore, on factorising, we get,
$ \Rightarrow \left( {a + 2} \right)\left( {a - 1} \right) = 0$
Therefore,
$ \Rightarrow a = - 2\,or\,1,$
But, $|x - 3|$ cannot be negative number because we have a mod sign, therefore, we cannot consider $|x - 3|$= -2, therefore,
\[ \Rightarrow x = 4,2\]
On opening the mod, we get,
\[ \Rightarrow x - 3 = \pm 1\]
On solving, we get,
\[ \Rightarrow x = 4,2\]
Therefore, the sum of all the real roots is 4+2=6.
Option D is the correct answer.
Note: While solving these questions, try to simplify the given equation and then find the roots by factoring or using the formula of finding the roots whichever method is easier for that particular question.
Given equation is $|x - 3{|^2} + |x - 3| - 2 = 0$
To simplify the equation, let us consider $|x - 3| = a$,
${a^2} + a - 2 = 0$
Therefore, on factorising, we get,
$ \Rightarrow \left( {a + 2} \right)\left( {a - 1} \right) = 0$
Therefore,
$ \Rightarrow a = - 2\,or\,1,$
But, $|x - 3|$ cannot be negative number because we have a mod sign, therefore, we cannot consider $|x - 3|$= -2, therefore,
\[ \Rightarrow x = 4,2\]
On opening the mod, we get,
\[ \Rightarrow x - 3 = \pm 1\]
On solving, we get,
\[ \Rightarrow x = 4,2\]
Therefore, the sum of all the real roots is 4+2=6.
Option D is the correct answer.
Note: While solving these questions, try to simplify the given equation and then find the roots by factoring or using the formula of finding the roots whichever method is easier for that particular question.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE