Question

Find whether the following equation have real roots. If real roots exist, find them.

`x^2 + 5sqrt(5)x - 70 = 0`

Answer 1

Given equation is `x^2 + 5sqrt(5)x - 70` = 0

On company with ax² + bx + c = 0, we get

a = 1, b = `5sqrt(5)` and c = – 70

∴ Discriminant, D = b² – 4ac

= `(5sqrt(5))^2 - 4(1)(-70)`

= 125 + 280

= 405 > 0

Therefore, the equation `x^2 + 5sqrt(5)x - 70` = 0 has two distinct real roots.

Roots, `x = (-b +- sqrt(D))/(2a)`

= `(-5sqrt(5) +- sqrt(405))/(2(1))`

= `(-5sqrt(5) +- 9sqrt(5))/2`

= `(-5sqrt(5) + 9 sqrt(5))/2, (-5sqrt(5) - 9sqrt(5))/2`

= `(4sqrt(5))/2, - (14 sqrt(5))/2`

= `2sqrt(5), -7sqrt(5)`