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 ax² + bx + c = 0, we get

a = 5, b = – 2 and c = – 10

∴ Discriminant, D = b² – 4ac

= (–2)² – 4(5)(–10)

= 4 + 200

= 204 > 0

Therefore, the equation 5x² – 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`