Question

What are the zero(s) `3x^2-7x+12=0`?

Answer 1

`3x^2-7x+12=0` has no zeros

Explanation:

For a parabolic equation in the form
`color(white)("XXX")ax^2+bx+c=0`
the discriminant
`color(white)("XXX) Delta = b^2-4ac`
indicates the number of zeros for the equation.

Specifically, in this case when
`color(white)("XXX")Delta < 0`
there are no solutions (i.e. no zeros)

For the given equation, you can see in the graph below that expression `3x^2-7x+12` never touches the X-axis (i.e. it is never equal to zero).
graph{3x^2-7x+12 [-13.75, 26.8, -2.68, 17.59]}
The discriminant is part of the quadratic formula which gives the solutions for equations of this type:
`color(white)("XXX")x =(-b+-sqrt(color(blue)(b^2-4ac)))/(2a)`
as you can see if the discriminant is zero then the solution would require the square root of a negative number
and the square root of a negative number does not exist as a Real value.