For quadratic
.. ax^2 +bx +c = 0
the discriminant is
.. d = b^2 -4ac
You have
.. a = 2
.. b = -5
.. c = 7
so the value of the discriminant for your equation is
.. (-5)^2 -4(2)(7)
.. = 25 -56
.. = -31
Because the discriminant is negative, the roots of the quadratic are complex.
Reasoning: this is the usual interpretation of the sign of the discriminant. It derives from the fact that the square root of the discriminant is part of the roots of the quadratic. That part will be imaginary when the discriminant is negative.
_____
The graph shows there are no real roots.
.. ax^2 +bx +c = 0
the discriminant is
.. d = b^2 -4ac
You have
.. a = 2
.. b = -5
.. c = 7
so the value of the discriminant for your equation is
.. (-5)^2 -4(2)(7)
.. = 25 -56
.. = -31
Because the discriminant is negative, the roots of the quadratic are complex.
Reasoning: this is the usual interpretation of the sign of the discriminant. It derives from the fact that the square root of the discriminant is part of the roots of the quadratic. That part will be imaginary when the discriminant is negative.
_____
The graph shows there are no real roots.