Answer

Verified

415.8k+ views

**Hint:**To solve this type of particular problem we use algebraic expression of square term.Let assume $9{x^4} - 12{x^3} + n{x^2} - 8x + 4$ = ${\left( {a{x^2} + bx + c} \right)^2}$.Expand the R.H.S term i.e assumed value by using formula ${\left( {x + y + z} \right)^2} = {x^2} + {y^2} + {z^2} + 2xy + 2yz + 2zx$.After substituting assumed value in formula we have to compare the similar terms to get our answer.

**Complete step-by-step answer:**

Let assume $9{x^4} - 12{x^3} + n{x^2} - 8x + 4$ = ${\left( {a{x^2} + bx + c} \right)^2}$

We assume this because the question says $9{x^4} - 12{x^3} + n{x^2} - 8x + 4$ is a perfect square.

Now we expand ${\left( {a{x^2} + bx + c} \right)^2}$by using formula ${\left( {x + y + z} \right)^2} = {x^2} + {y^2} + {z^2} + 2xy + 2yz + 2zx$

So ${\left( {a{x^2} + bx + c} \right)^2} = {a^2}{x^4} + {b^2}{x^2} + {c^2} + 2ab{x^3} + 2bcx + 2ac{x^2}$

Now ${a^2}{x^4} + {b^2}{x^2} + {c^2} + 2ab{x^3} + 2bcx + 2ac{x^2}$=$9{x^4} - 12{x^3} + n{x^2} - 8x + 4$

So now we compare terms

Firstly comparing ${x^4}$ we get ${a^2} = 9$

And $a = \pm 3$

Now compare constant term ${c^2} = 4$

And $c = \pm 2$

Now comparing ${x^3}$ term we get

$2ab = - 12$

And $ab = - 6$

Now we have to put value of $a$ so that we get

$b = \pm 2$

Now comparing ${x^2}$ we get

$2ac + {b^2} = n$

Now we have to put the value of a,b,c in the above equation to find the value of n.

$2 \times 3 \times 2 + {\left( { \pm 2} \right)^2}=n$

So the square of any number is always positive

$12 + 4$

$n = 16$

The value of $n = 16$

**So, the correct answer is “Option B”.**

**Note:**In this type of question we have to remember all the algebraic expressions and formulas that how we can use them .We have to compare all the similar terms and remember whenever we solve a square term we have to always use \[ \pm \] both signs so that we get all possible values that we need.

Recently Updated Pages

Differentiate between Shortterm and Longterm adapt class 1 biology CBSE

How do you find slope point slope slope intercept standard class 12 maths CBSE

How do you find B1 We know that B2B+2I3 class 12 maths CBSE

How do you integrate int dfracxsqrt x2 + 9 dx class 12 maths CBSE

How do you integrate int left dfracx2 1x + 1 right class 12 maths CBSE

How do you find the critical points of yx2sin x on class 12 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Define limiting molar conductivity Why does the conductivity class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Name 10 Living and Non living things class 9 biology CBSE

The Buddhist universities of Nalanda and Vikramshila class 7 social science CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE