# the roots of the quadratic equation 6x^2-x-2=0 are

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__Answer____ ____:____-____ __

2/3 , -1/2

__Given____ ____:____-____ __

6x² -x -2 = 0

__To____ ____find____ ____:____-____ __

Roots of the Quadratic equation

__SOLUTION____ ____ ____:____-____ __

__Method____ ____-____ ____1____ ____:____-____ __

By factorisation method splitting the midlle term

6x² -x -2 = 0

*Here**sum**of**two**numbers**should**be**-1**x**and**product**of**two**numbers**should**be**-12x**²*

So, the numbers are

**3x**** ****×**** ****-4x**** ****=**** ****-12x****²**

**3x****+****(****-4x****)**** ****=**** ****3x-4x**

** **** **** **** **** **** **** **** **** **** ****=**** ****-1x**

So, split the middle term as 3x -4x

6x² -x -2 = 0

6x² + 3x -4x -2 = 0

3x(2x +1) -2(2x +1) = 0

(2x +1) (3x -2) = 0

2x +1 =0

2x = -1

### x = -1/2

3x -2 =0

3x = 2

### x = 2/3

So, the roots are -1/2, 2/3

__Method____ ____-2____ ____:____-____ __

Solving by the Quadratic formula

6x² -x - 2=0

Comparing with general form of Quadratic equation ax² + bx + c = 0

- a = 6
- b = -1
- c = -2

Substituting the values in formula

So, the value of x are 2/3 , -1/2

So, the roots of Quadratic equation is 2/3 , -1/2

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