Question

Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.

Answer 1

Given:

The quadratic equation is:

`12a^2+9a+7=0`

To find:

The solution of the given equation in simplest form by using the quadratic formula.

Solution:

If a quadratic equation is
`ax^2+bx+c=0`, then the quadratic formula is:

`x=(-b\pm √(b^2-4ac))/(2a)`

We have,

`12a^2+9a+7=0`

Here,
`a=12,b=9,c=7`. Using the quadratic formula, we get

`x=(-(9)\pm √((9)^2-4(12)(7)))/(2(12))`

`x=(-9\pm √(81-336))/(24)`

`x=(-9\pm √(-255))/(24)`

`x=(-9\pm i√(255))/(24)`
`[\because √(-a)=i√(a)]`

The solutions of the given equations are
`x=(-9-i√(255))/(24)` and
`x=(-9+i√(255))/(24)`.

Therefore, the correct option is B.