Question

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

5x² – 2x – 10 = 0

Answer 1

Given equation is 5x² – 2x – 10 = 0

On company with `ax^2 + bx + c` = 0, we get

a = 5, b = – 2 and c = – 10

∴ Discriminant, D = `b^2 - 4ac`

= `(-2)^2 - 4(5)(-10)`

= 4 + 200

= 204 > 0

Therefore, the equation `5x^2 - 2x - 10` = 0 has two distinct real roots.

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

= `(-(-2) +- sqrt(204))/(2 xx 5)`

= `(2 +- 2sqrt(51))/10`

= `(1 +- sqrt(51))/5`

= `(1 + sqrt(51))/5, (1 - sqrt(51))/5`