Question

How do you find the zeros, real and imaginary, of `y= 3x^2+4x+2` using the quadratic formula?

Answer 1

Substitute the coefficients into the equation and evaluate.

Explanation:

The quadratic equation is `x=\frac{-b\pm\sqrt{b^2-4ac\ }}{2a}`
In the example a = 3, b = 4 and c = 2

`x = (-4 +- sqrt(4^2 - 4*3*2))/(2*3)`
`x= (-4 +- sqrt(16 - 24))/6`
`x = -4/6 +- sqrt(-8)/6`
`x = -2/3(1 +sqrt(-2))` or `-2/3(1 - sqrt(-2))`

The equation only has imaginary roots. The graph never touches or crosses the x axis.