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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

A
The roots of the given quadratic equation are 13 and 1.
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B
The roots of the given quadratic equation are 25 and 5.
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C
The roots of the given quadratic equation are 12 and 3.
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D
The roots of the given quadratic equation are 27 and 4.
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Solution

The correct option is B The roots of the given quadratic equation are 12 and 3.
Given equation is 2x27x+3=0
(x272x72x+(72)2)(72)2+6=0
(x72)2494+6=0
(x72)2254=0
(2x72)2=254
2x72=±254
2x72=±52
2x72=52 or 2x72=52
2x=52+72 or 2x=52+72
2x=6 or 2x=1
x=3 or x=12
Thus, the roots are 3 and 12.

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