Question

Find the roots of the following equation, if they exist, by applying the quadratic formula:

2x² + x – 4 = 0

Answer 1

The given equation is 2x² + x – 4 = 0

Comparing it with ax² + bx + c = 0 we get 

a = 2, b = 1 and c = –4 

∴ Discriminant, D = b² – 4ac

= (1)² – 4 × 2 × (–4)

= 1 + 32

= 33 > 0 

So, the given equation has real roots.

Now, `sqrt(D) = sqrt(33)` 

∴ `α = (-b + sqrt(D))/(2a)`

= `(-1 + sqrt(33))/(2 xx 2)`

= `(-1 + sqrt(33))/4` 

∴ `β = (-b - sqrt(D))/(2a)`

= `(-1 - sqrt(33))/(2 xx 2)`

= `(-1 - sqrt(33))/4` 

Hence, `((-1+sqrt(33)))/4` and `((-1 - sqrt(33)))/4` are the roots of the given equation.