Answer
Verified
426.6k+ views
Hint: Factorisation is a method of expressing or writing a given number in the form of the product of other numbers. The numbers present in the product are called as factors of the original number.
Complete step by step solution:
Let us first understand what is meant by the term factorisation.Factorisation is a method of expressing or writing a given number in the form of the product of other numbers. The numbers present in the product are called as factors of the original number.For example, the number 6 can be written in the form of the product of the numbers 2 and 3. i.e. $6=3\times 2$. Here, 3 and 2 are the factors of 6. The method of factorisation can also be used for expressions containing variables.
Here, the expression is given as $2{{x}^{2}}-x-6$ …. (i).
We can write the expression (i) as $2{{x}^{2}}-x-6=2{{x}^{2}}-4x+3x-6$.
Now, we can take the term ‘2x’ as common from the first two terms and 3 as common from the second two terms as shown below.
$2{{x}^{2}}-x-6=2x(x-2)+3(x-2)$.
Now, take the term (x - 2) as a common term. Then,
$2{{x}^{2}}-x-6=(x-2)(2x+3)$
Therefore, we factored the expression.
But, it is given that $2{{x}^{2}}-x-6=0$.
Then this means that $(x-2)(2x+3)=0$
This means that either $x-2=0$ or $2x+3=0$
If we further simplify, then we get that either $x=2$ or $x=-\dfrac{3}{2}$.
Therefore, the roots or the solutions of the given quadratic equation are $x=2$ or $x=-\dfrac{3}{2}$.
Note: Here is a trick to solve a given quadratic equation with factorisation method.When we use factorisation method, we must split the middle term of the expression in two terms such that the sum of the two terms is equal to the middle terms and product of the two is equal to product of the other terms.
Complete step by step solution:
Let us first understand what is meant by the term factorisation.Factorisation is a method of expressing or writing a given number in the form of the product of other numbers. The numbers present in the product are called as factors of the original number.For example, the number 6 can be written in the form of the product of the numbers 2 and 3. i.e. $6=3\times 2$. Here, 3 and 2 are the factors of 6. The method of factorisation can also be used for expressions containing variables.
Here, the expression is given as $2{{x}^{2}}-x-6$ …. (i).
We can write the expression (i) as $2{{x}^{2}}-x-6=2{{x}^{2}}-4x+3x-6$.
Now, we can take the term ‘2x’ as common from the first two terms and 3 as common from the second two terms as shown below.
$2{{x}^{2}}-x-6=2x(x-2)+3(x-2)$.
Now, take the term (x - 2) as a common term. Then,
$2{{x}^{2}}-x-6=(x-2)(2x+3)$
Therefore, we factored the expression.
But, it is given that $2{{x}^{2}}-x-6=0$.
Then this means that $(x-2)(2x+3)=0$
This means that either $x-2=0$ or $2x+3=0$
If we further simplify, then we get that either $x=2$ or $x=-\dfrac{3}{2}$.
Therefore, the roots or the solutions of the given quadratic equation are $x=2$ or $x=-\dfrac{3}{2}$.
Note: Here is a trick to solve a given quadratic equation with factorisation method.When we use factorisation method, we must split the middle term of the expression in two terms such that the sum of the two terms is equal to the middle terms and product of the two is equal to product of the other terms.
Recently Updated Pages
Identify the feminine gender noun from the given sentence class 10 english CBSE
Your club organized a blood donation camp in your city class 10 english CBSE
Choose the correct meaning of the idiomphrase from class 10 english CBSE
Identify the neuter gender noun from the given sentence class 10 english CBSE
Choose the word which best expresses the meaning of class 10 english CBSE
Choose the word which is closest to the opposite in class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
10 examples of friction in our daily life
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What is pollution? How many types of pollution? Define it