Question

# Using the method of completion of squares find one of the roots of the equation 2x2−7x+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, (x−74)2−2516=0 2x2−7x+3=0 Dividing by the coefficient of x2, we get x2−72x+32=0; a=1, b=72, c=32 Adding and subtracting the square of b2=74, (half of coefficient of x) we get, [x2−2(74)x+(74)2]−(74)2+32=0 The equation after completing the square is : (x−74)2−2516=0 Taking square root, (x−74)=(±54) Taking positive sign 54, x=3 Taking negative sign −54, x=12

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