Question

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

15x² – 28 = x

Answer 1

Given: 

15x² – 28 = x

⇒ 15x² – x – 28 = 0 

On comparing it with ax² + bx + c = 0 we get; 

a = 25, b = –1 and c = –28 

Discriminant D is given by:

D = (b² – 4ac) 

= (–1)² – 4 × 15 × (–28) 

= 1 – (–1680) 

= 1 + 1680 

= 1680

= 1681 > 0 

Hence, the roots of the equation are real.

Roots α and β are given by: 

`α = (-b + sqrt(D))/(2a)`

= `(-(-1) + sqrt(1681))/(2 xx 25)`

= `(1 + 41)/30`

= `42/30`

= `7/5` 

 `β = (-b - sqrt(D))/(2a)`

= `(-(-1)- sqrt(1681))/(2 xx 25)`

= `(1 - 41)/30`

= `(-40)/30`

= `(-4)/3` 

Thus, the roots of the equation are `7/5` and `(-4)/3`.