Question

What are the solutions of the equation?

12X^2+11X-5=0

a. 5/4, 1/3
b. -5/4, -1/3
c. -5/4, 1/3
d. 5/4, -1/3

Answer 1

Option (C) is correct.

The solution of the quadratic equation
`12x^2+11x-5=0` is
`x=(1)/(3)` and
`x=(-5)/(4)`

Explanation:

Consider the given quadratic equation
`12x^2+11x-5=0`

We can solve the quadratic equation using middle term splitting method,

11x can be written as 15x-4x , we get,

`\Rightarrow 12x^2+11x-5=0`

`\Rightarrow12x^2+15x-4x-5=0`

Taking terms common, we get,

`\Rightarrow3x(4x+5)-1(4x+5)=0`

Thus,
`\Rightarrow (3x-1)(4x+5)=0`

Thus, we get
`\Rightarrow (3x-1)=0` or
`\Rightarrow (4x+5)=0`

this gives
`\Rightarrow x=(1)/(3)` or
`\Rightarrow x=(-5)/(4)`

Thus, the solution of the quadratic equation
`12x^2+11x-5=0` is
`x=(1)/(3)` and
`x=(-5)/(4)`