Question

Solve this quadratic equation using the quadratic formula.

3x 2 + 5x + 1 = 0

Answer 1

`x=(-√(13) -5)/(6)` or
`x=(√(13) -5)/(6)`

Explanation:

The given quadratic equation is

`3x^2+5x+1=0`

When we compare to the general quadratic equation,

`ax^2+bx+c=0`, then we have

`a=3,b=5,c=1`

The quadratic formula is given by,

`x=(-b\pm √(b^2-4ac) )/(2a)`

We substitute the given values into the formula to obtain,

`x=(-5\pm √(5^2-4(3)(1)) )/(2(3))`

This simplifies to,

`x=(-5\pm √(25-12) )/(2(3))`

This further simplifies to,

`x=(-5\pm √(13) )/(6)`

We split the plus or minus sign to obtain,

`x=(-√(13) -5)/(6)` or
`x=(√(13) -5)/(6)`