Answer

Verified

372.9k+ views

**Hint:**We first make the coefficient of \[{x^2}\]as 1 by dividing the complete equation by the coefficient of \[{x^2}\]. Then shift the constant value to the right hand side of the equation. Add the square of half value of coefficient of ‘x’ on both sides of the equation. Afterwards we can simplify this using some simple algebraic identity and by taking LCM we will get the desired result.

**Complete step-by-step solution:**

Given, \[{x^2} - 2x - 120 = 0\].

We can see that the coefficient of \[{x^2}\] is 1. So no need to divide the equation by the coefficient of \[{x^2}\].

The next step is we need to shift the constant terms to the right hand side of the equation,

\[{x^2} - 2x = 120{\text{ }} - - - - (1)\].

Now we can see that the coefficient of ‘x’ is \[ - 2\]. We divide the coefficient of ‘x’ by 2 and we square it.

\[{\left( {\dfrac{{ - 2}}{2}} \right)^2} = {( - 1)^2} = 1\].

Now we need to add ‘1’ on both sides of the equation (1).

\[{x^2} - 2x + 1 = 120 + 1\]

We know the algebraic identity \[{(a - b)^2} = {a^2} - 2ab + {b^2}\]. Comparing this with the left hand side of an equation we have \[a = x\] and \[b = 1\].

\[ \Rightarrow {\left( {x - 1} \right)^2} = 120 + 1\]

\[ \Rightarrow {\left( {x - 1} \right)^2} = 121\]

Taking square root on both side we have,

\[ \Rightarrow \left( {x - 1} \right) = \pm \sqrt {121} \]

\[ \Rightarrow \left( {x - 1} \right) = \pm 11\]

That is we have two roots,

\[ \Rightarrow \left( {x - 1} \right) = 11\] and \[\left( {x - 1} \right) = - 11\]

\[ \Rightarrow x = 11 + 1\] and \[x = - 11 + 1\]

\[ \Rightarrow x = 12\] and \[x = - 10\], is the required solution.

**Note:**Since we have a polynomial of degree two and hence it is called quadratic polynomial. If we have a polynomial of degree ‘n’ then we have ‘n’ roots. In the given problem we have a degree that is equal to 2. Hence the number of roots are 2. Also keep in mind when shifting values from one side of the equation t0 another side of the equation, always change sign from positive to negative and vice-versa.

Recently Updated Pages

The base of a right prism is a pentagon whose sides class 10 maths CBSE

A die is thrown Find the probability that the number class 10 maths CBSE

A mans age is six times the age of his son In six years class 10 maths CBSE

A started a business with Rs 21000 and is joined afterwards class 10 maths CBSE

Aasifbhai bought a refrigerator at Rs 10000 After some class 10 maths CBSE

Give a brief history of the mathematician Pythagoras class 10 maths CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

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

Name 10 Living and Non living things class 9 biology CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

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

Write the 6 fundamental rights of India and explain in detail