determine whether the given value of x is the root of given quadratic equation 6x^2-x-2x=0,x=3/2​

1 thought on “determine whether the given value of x is the root of given quadratic equation 6x^2-x-2x=0,x=3/2​”

1. [tex]\sf\huge\bold{\underline{\underline{{Solution}}}}[/tex]

   We have given a quadratic equation

   firstly we factorise it and then check whether the given value are the roots or not.

   ➜6x²-x-2

   ➜6x²-4x+3x-2

   ➜2x(3x-2)+1(3x-2)

   ➜(2x+1)(3x-2)

   put values equal to zero

   ➜2x+1=0

   ➜x=-1/2

   ➜3x-2=0

   ➜x=2/3

   Hence,the above given values are not the roots of the given equation.

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   Check:

   You can simply find whether the given values are the roots of the given equation or not by putting into the Equation.

   At x=0

   ➜6x²-x-2=0

   ➜6(0)²-0-2

   ➜-2 ≠0.

   At x= 3/2

   ➜6(3/2)²-3/2-2

   ➜6(9/4)-3/2-2

   ➜54/4-3/2-2

   ➜27/2-3/2-2

   ➜24/2-2

   ➜12-2

   ➜10≠0

   Hence,we see that both values not satisfied the Equation.

   Now Check with the roots we find

   At x= -1/2

   ➜6x²-x-2

   ➜6(-1/2)2-(-1/2)-2

   ➜6/4+1/2-2

   ➜3/2+1/2-2

   ➜4/2-2

   ➜2-2=0

   At x= 2/3

   ➜6x²-x-2

   ➜6(2/3)²-2/3-2

   ➜24/9-2/3-2

   ➜24-6/9-2

   ➜18/9-2

   ➜2-2=0

   Both values satisfied the Equation.

   Hence,the roots are -1/2 and 2/3.

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