
Give the factors and solution of the expression \[3{x^2} - 27 = 0\]by any mathematical method?
Answer
444.6k+ views
Hint:Here we have to factorize the question by using mathematical properties, such a quadratic equation can also be solved by the sridharacharya rule, and here you can use them for finding the solution of the equation. For finding factors you have to rearrange the term so as to obtain the factors by taking common or doing some adjustments.
Complete step by step answer:
Here, for the given equation we have to do some rearrangement by taking common of the number which is common in both terms, and then we can easily see that it is becoming an equation which can be easily solved by algebraic identity say:
\[ \Rightarrow {a^2} - {b^2} = (a + b)(a - b)\]
On solving we get:
\[3{x^2} - 27 = 0 \\
\Rightarrow 3({x^2} - 9) = 0 \\
\Rightarrow 3({x^2} - {3^2}) = 0 \\
\Rightarrow 3(x - 3)(x + 3) = 0 \\
\Rightarrow (x - 3)(x + 3) = 0 \\
\therefore x = 3, - 3 \]
So the solution for the above equation is \[3, - 3\].
Hence, the factors of the equation are \[(x + 3),(x - 3)\].
Additional Information:
Mid term split method is easy to find, but here it cant be applied because in the mid term equation the middle term is needed to break it into two parts to obtain the conditions but here for this question the middle term is not present.
Note: In two variable questions it will work but make the question very complicated, so you have to be careful while using the highest common factor method. This method is fast and easy to use but is applicable to certain specific question only and in this question it can be applied very easily.Example of this method could be a three variable algebraic equation like: \[xyz + xy \]
Complete step by step answer:
Here, for the given equation we have to do some rearrangement by taking common of the number which is common in both terms, and then we can easily see that it is becoming an equation which can be easily solved by algebraic identity say:
\[ \Rightarrow {a^2} - {b^2} = (a + b)(a - b)\]
On solving we get:
\[3{x^2} - 27 = 0 \\
\Rightarrow 3({x^2} - 9) = 0 \\
\Rightarrow 3({x^2} - {3^2}) = 0 \\
\Rightarrow 3(x - 3)(x + 3) = 0 \\
\Rightarrow (x - 3)(x + 3) = 0 \\
\therefore x = 3, - 3 \]
So the solution for the above equation is \[3, - 3\].
Hence, the factors of the equation are \[(x + 3),(x - 3)\].
Additional Information:
Mid term split method is easy to find, but here it cant be applied because in the mid term equation the middle term is needed to break it into two parts to obtain the conditions but here for this question the middle term is not present.
Note: In two variable questions it will work but make the question very complicated, so you have to be careful while using the highest common factor method. This method is fast and easy to use but is applicable to certain specific question only and in this question it can be applied very easily.Example of this method could be a three variable algebraic equation like: \[xyz + xy \]
Recently Updated Pages
What percentage of the area in India is covered by class 10 social science CBSE

The area of a 6m wide road outside a garden in all class 10 maths CBSE

What is the electric flux through a cube of side 1 class 10 physics CBSE

If one root of x2 x k 0 maybe the square of the other class 10 maths CBSE

The radius and height of a cylinder are in the ratio class 10 maths CBSE

An almirah is sold for 5400 Rs after allowing a discount class 10 maths CBSE

Trending doubts
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Why is there a time difference of about 5 hours between class 10 social science 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

Explain the Treaty of Vienna of 1815 class 10 social science CBSE

Write an application to the principal requesting five class 10 english CBSE
