Q1.tell whether the given value of x is the root of given quadratic equation 6x^2-x-2x=0,x=3/2.
Answers
Explanation:
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.
Answer:
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