Question

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

25x² + 30x + 7 = 0

Answer 1

Given:

25x² + 30x + 7 = 0

On comparing it with ax² + bx + x = 0 

a = 25, b = 30 and c = 7

Discriminant D is given by: 

D = (b² – 4ac) 

= 30² – 4 × 25 × 7 

= 900 – 700 

= 200

= 200 > 0 

Hence, the roots of the equation are real.

Roots α and β are given by: 

`α = (-b + sqrt(D))/(2a)`

= `(-30 + sqrt(200))/(2 xx 25)`

= `(-30 + 10sqrt(20))/50`

= `(10(-3 + sqrt(2)))/50`

= `((-3 + sqrt(2)))/5` 

`β = (-b - sqrt(D))/(2a)`

= `(-30 - sqrt(200))/(2 xx 25)`

= `(-30 - 10sqrt(20))/50`

= `(10(-3 - sqrt(2)))/50`

= `((-3 - sqrt(2)))/5` 

Thus, the roots of the equation are `((-3 + sqrt(2)))/5` and `((-3 - sqrt(2)))/5`.