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

a = –2, b = 3 and c = 2

∴ Discriminant, D = `b^2 - 4ac`

= `(3)^2 - 4 - (-2)(2)`

= 9 + 16

= 25 > 0

Therefore, the equation `-2x^2 + 3x + 2` = 0 has two distinct real roots because we know that if the equation `ax^2 + 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`