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Question

Using the method of completion of squares find one of the roots of the equation 2x27x+3=0. Also, find the equation obtained after completion of the square.


A

6, (x74)22516=0

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B

3, (x74)22516=0

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C

3, (x72)22516=0

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D

13, (x72)22516=0

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Solution

The correct option is B

3, (x74)22516=0


2x27x+3=0
Dividing by the coefficient of x2, we get
x272x+32=0; a=1, b=72, c=32

Adding and subtracting the square of b2=74, (half of coefficient of x)

we get,
[x22(74)x+(74)2](74)2+32=0

The equation after completing the square is :
(x74)22516=0

Taking square root, (x74)=(±54)
Taking positive sign 54, x=3
Taking negative sign 54, x=12


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