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Question

Find the roots of the equation 5x26x2=0 by completion of the square method.

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Solution

5x2 – 6x – 2 = 0 ……………………………. (1)

On multiplying (1) by 5, we get 25x2 - 30x -10 = 0

(5x)2 - 2(5x)(3) +9 - 9 – 10 = 0

(5x3)2 = 19

Taking square root on both sides, we get

5x – 3 = ±19

5x = ±19

5x = 3 + 19 5x = 3 - 19

x = (3 + 19)/5 x = (3 - 19)/5

Therefore (3 + 19)/5 and (3 - 19)/5 are the roots of the given quadratic equation.


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