Question

find out the root of equation 2 x square minus x minus 3 is equal to zero​

Answer 1

The roots of the equation are - 1 , 3/2

Given :

The equation 2x² - x - 3 = 0

To find :

The roots of the equation

Solution :

Step 1 of 2 :

Write down the given equation

Here the given equation is 2x² - x - 3 = 0

Step 2 of 2 :

Find the roots of the equation

$\displaystyle \sf{ 2 {x}^{2} - x - 3 = 0}$

$\displaystyle \sf{ \implies 2 {x}^{2} - (3 - 2)x - 3 = 0}$

$\displaystyle \sf{ \implies 2 {x}^{2} - 3x + 2x - 3 = 0}$

$\displaystyle \sf{ \implies x(2x - 3) + 1(2x - 3) = 0}$

$\displaystyle \sf{ \implies (x + 1)(2x - 3) = 0}$

Now ,

$\displaystyle \sf{ x + 1 = 0 \: \: gives \: \: x = - 1 }$

$\displaystyle \sf{2 x - 3 = 0 \: \: gives \: \: x = \frac{3}{2} }$

Hence roots of the equation are - 1 , 3/2

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Answer 2

Answer:

The roots of the equation are $x=-1,\frac{3}{2}$.

Explanation:

Concept: The "solutions" or numerical values that are equal to the given equation's variable are known as the roots of the equation.

Given : The equation $2x^{2} - x - 3 = 0$

To find : The roots of the given equation.

Solution :

Here the given equation is,

$2x^{2} - x - 3 = 0$

To find the roots of the equation factorize the middle term as shown below:

$2x^{2} - x - 3 = 0\\2x^{2} -3x+2x - 3 = 0\\x(2x-3)+1(2x-3)=0\\(x+1)(2x-3)=0$

Now put these values equal to one to get the root values.

$x+1=0\\x=-1\\2x-3=0\\2x=3\\x=\frac{3}{2}$

The roots of the equation are $x=-1,\frac{3}{2}$.

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