# Solve \[ - 2{x^2} + 5x - 2 = 0\]

Answer

Verified

183.3k+ views

**Hint**: According to the given question, the equation \[ - 2{x^2} + 5x - 2 = 0\] in the form of \[a{x^2} + bx + c = 0\] . Then, find out the product which is equal to ac and sum which is equal to b. Then use the splitting the middle term method to factorise the equation and then find the roots of the equation.

**:**

__Complete step-by-step answer__As, it is given \[ - 2{x^2} + 5x - 2 = 0\]

Here, by using splitting the middle term method we can calculate the factors of the equation \[ - 2{x^2} + 5x - 2 = 0\]

In this method we will find out two numbers whose sum is \[5\] and product is \[4\] .

So, we are getting the two numbers which are \[4\] and \[1\] .

Now, solving with equation: \[ - 2{x^2} + 5x - 2 = 0\]

Splitting the \[5x\] into two numbers as \[4x + x\]

We get,

\[ - 2{x^2} + 4x + x - 2 = 0\]

Taking out common in the pairs of 2 we get,

\[ - 2x\left( {x - 2} \right) + 1\left( {x - 2} \right) = 0\]

Taking 2 same factors one time we get,

\[\left( { - 2x + 1} \right)\left( {x - 2} \right) = 0\]

Now we will solve these two factors separately,

one factor as

\[ - 2x + 1 = 0\]

Taking 1 from left hand side to right hand side we get,

\[ - 2x = - 1\]

Cancelling negative side from both left and right hand side we get,

\[2x = 1\]

Dividing both left and right hand side by 4 we get the value of x that is,

\[x = \dfrac{1}{2}\]

Other factor as,

\[x - 2 = 0\]

Taking 2 from left hand side to right hand side we get,

\[x = 2\]

Hence, after solving the equation \[ - 2{x^2} + 5x - 2 = 0\] the value of \[x = 2,\dfrac{1}{2}\]

**So, the correct answer is “\[x = 2,\dfrac{1}{2}\]”.**

**Note**: To solve these types of questions we can either use the formula that is \[x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\] in which the equation must be in the form of \[a{x^2} + bx + c = 0\] to find the roots of the equation or by using splitting the middle term method you can also calculate the factors if the equation is not given equal to zero as well as the value of x or roots of the equation as shown above.

Recently Updated Pages

If ab and c are unit vectors then left ab2 right+bc2+ca2 class 12 maths JEE_Main

A rod AB of length 4 units moves horizontally when class 11 maths JEE_Main

Evaluate the value of intlimits0pi cos 3xdx A 0 B 1 class 12 maths JEE_Main

Which of the following is correct 1 nleft S cup T right class 10 maths JEE_Main

What is the area of the triangle with vertices Aleft class 11 maths JEE_Main

The coordinates of the points A and B are a0 and a0 class 11 maths JEE_Main

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

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

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

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

Name the Largest and the Smallest Cell in the Human Body ?