Answer
Verified
417.3k+ 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
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Which type of bond is stronger ionic or covalent class 12 chemistry CBSE
What organs are located on the left side of your body class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE
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
When people say No pun intended what does that mea class 8 english CBSE