Question

Solve the following quadratic equation 2x² − 5x − 4 = 0.

Answer 1

Given the quadratic equation

2x² − 5x − 4 = 0 

Comparing it with the standard form ax² + bx + c, we get:

a = 2, b = −5, c = − 4

Using the quadratic formula,

`x = (−b ± sqrt(b^2 − 4ac))/(2a)`

The discriminant is calculated as:

D = b2 − 4ac

= (−5)² − 4 × 2 × (−4)

= 25 + 32 = 57

For the positive sign, 

x = `(5 + sqrt57)/4`

For the positive sign,

x = `(5 + sqrt57)/4`

x = `(5 + 7.549)/4`

x = 3.137

For the negative sign,

x = `(5 − sqrt57)/4`

x = `(5 − 7.549)/4`

x = − 0.637

Hence, the values of x are 3.137 and −0.637.