Question

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

8x² + 2x – 3 = 0

Answer 1

Given equation is 8x² + 2x – 3 = 0

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

a = 8, b = 2 and c = – 3

∴ Discriminant, D = b² – 4ac

= (2)² – 4(8)(– 3)

= 4 + 96

= 100 > 0

Therefore, the equation 8x² + 2x – 3 = 0 has two distinct real roots because we know that,

If the equation ax² + bx – c = 0 has discriminant greater than zero, then it has two distinct real roots.

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

= `(-2 +- sqrt(100))/16`

= `(-2 +- 10)/16`

= `(-2 + 10)/16, (-1 - 10)/16`

= `8/16, -12/16`

= `1/2, - 3/4`