Question

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

–2x² + 3x + 2 = 0

Answer 1

Given equation is –2x² + 3x + 2 = 0

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

a = –2, b = 3 and c = 2

∴ Discriminant, D = b² – 4ac

= (3)² – 4 – (–2)(2)

= 9 + 16

= 25 > 0

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

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

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

= `(-3 +- sqrt(25))/(2(-2))`

= `(-3 +- 5)/(-4)`

= `(-3 + 5)/(-4), (-3 - 5)/(-4)`

= `2/(-4), (-8)/(-4)`

= `- 1/2, 2`