Question

Find the roots of the equation $5x^2–6x–2=0$ by completion of the square method.

Answer 1

$5x^2$ – 6x – 2 = 0 ……………………………. (1)

On multiplying (1) by 5, we get 25$x^2$ - 30x -10 = 0

$(5x{)}^2$ - 2(5x)(3) +9 - 9 – 10 = 0

$(5x–3{)}^2$ = 19

Taking square root on both sides, we get

5x – 3 = $\pm \surd 19$

5x = $\pm \surd 19$

5x = 3 + $\surd 19$ 5x = 3 - $\surd 19$

x = (3 + $\surd 19$)/5 x = (3 - $\surd 19$)/5

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