Question

The solution set for the equation, 25x (x + 1) = – 4, is ______.

Options

• `{1/5, 4/5}`

• `{-1/5, 4/5}`

• `{-4/5, -1/5}`

• `{-4/5, 1/5}`

Answer 1

The solution set for the equation, 25x (x + 1) = – 4, is `underlinebb({-4/5, -1/5})`.

Explanation:

25x (x + 1) = – 4

⇒ 25x² + 25x + 4 = 0

Use the quadratic formula:

`x = (-25 ± sqrt(25^2 - 4 xx 25 xx 4))/(2 xx 25)` 

= `(-25 ± sqrt(625 - 400))/50`

= `(-25 ± 15)/50` 

So, `x = (-25 + 15)/50` 

= `(-10)/50` 

= `(-1)/5`

or

`x = (-25 - 15)/50` 

= `(−40)/50`

= `(-4)/5` 

Both satisfy the original equation, so the solution set is `{-4/5, -1/5}`.