Answer
Verified
480.3k+ views
Hint: In this question L.H.S of the given equation is a square of real numbers, so the square of real number is always positive or non-negative so, R.H.S part of the given equation should be positive, so use this concept to get the solution of the question.
Given equation is
${y^2} = \left( {x - 1} \right){\left( {x - 2} \right)^2}$
We have to prove for what value of x the above function is not defined.
As we know that the square of any real number is non-negative.
So, above curve is not defined if R.H.S is negative
So, R.H.S of above curve is
$\left( {x - 1} \right){\left( {x - 2} \right)^2}$
$ \Rightarrow \left( {x - 1} \right){\left( {x - 2} \right)^2} < 0$………………. (1), (Condition of not defined)
As we see from above equation
${\left( {x - 2} \right)^2} \geqslant 0$ for any value of x.
i.e. ${\left( {x - 2} \right)^2} \geqslant 0{\text{ }}\forall \left( {x \in R} \right)$ , where R is a real number.
Therefore from equation (1)
$\left( {x - 1} \right) < 0$
$\therefore x < 1$
Therefore for x is less than 1 curve is not defined.
Say $x = 0.9$,
Therefore given equation converts
$
{y^2} = \left( {0.9 - 1} \right){\left( {0.9 - 2} \right)^2} = \left( { - 0.1} \right){\left( { - 1.1} \right)^2} = - 0.1\left( {1.21} \right) = - 0.121 \\
\Rightarrow y = \sqrt { - 0.121} \\
$
So, as we see, the square root of a negative number is not defined.
Hence option (D) is correct.
Note: Whenever we face such types of questions always remember the condition of square of any real number which is square of any real number is non negative so, find out for what values of x R.H.S part of given equation is negative as above which is the required answer for which the given function is not defined.
Given equation is
${y^2} = \left( {x - 1} \right){\left( {x - 2} \right)^2}$
We have to prove for what value of x the above function is not defined.
As we know that the square of any real number is non-negative.
So, above curve is not defined if R.H.S is negative
So, R.H.S of above curve is
$\left( {x - 1} \right){\left( {x - 2} \right)^2}$
$ \Rightarrow \left( {x - 1} \right){\left( {x - 2} \right)^2} < 0$………………. (1), (Condition of not defined)
As we see from above equation
${\left( {x - 2} \right)^2} \geqslant 0$ for any value of x.
i.e. ${\left( {x - 2} \right)^2} \geqslant 0{\text{ }}\forall \left( {x \in R} \right)$ , where R is a real number.
Therefore from equation (1)
$\left( {x - 1} \right) < 0$
$\therefore x < 1$
Therefore for x is less than 1 curve is not defined.
Say $x = 0.9$,
Therefore given equation converts
$
{y^2} = \left( {0.9 - 1} \right){\left( {0.9 - 2} \right)^2} = \left( { - 0.1} \right){\left( { - 1.1} \right)^2} = - 0.1\left( {1.21} \right) = - 0.121 \\
\Rightarrow y = \sqrt { - 0.121} \\
$
So, as we see, the square root of a negative number is not defined.
Hence option (D) is correct.
Note: Whenever we face such types of questions always remember the condition of square of any real number which is square of any real number is non negative so, find out for what values of x R.H.S part of given equation is negative as above which is the required answer for which the given function is not defined.
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