Question

How do you find the roots, real and imaginary, of `y= 4x^2 - 15x + 32` using the quadratic formula?

Answer 1

Imaginary.

Explanation:

Set the RHS equal to 0 and solve for x using quadratic formula. Accordingly,
`x= (15 +- sqrt(15^2 -4*4*32))/(2*4)`

The number inside the radical sign would be -287. Since square root of a negative number is imaginary, hence the roots of the given function would be imaginary. The import of this conclusion is that the vertical parabola, which this function represents, would not cross the x- axis.