Question

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

Answer 1

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

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.