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Question

Find the roots of the following quadratic equations, if they exist, by the method of completing the square:
2x27x+3=0

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Solution

(i) 2x27x+3=0
We know;
D=b24ac
= (7)24×2×3
= 4924
= 25
Since D>0, roots are possible for this equation.
2x27x=3
On dividing both sides of the equation by 2, we get,
x27x2=32
x22×x×74=32
On adding (74)2 to both sides of equation, we get
(x)22×x×74+(74)2=(74)232
(x74)2=491632
(x74)2=2516
(x74)=±54
x=74±54
x=74+54 or x=7454
x=124 or x=24
x=3 or 12


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