Which quadratic graph below has a negative discriminant?

The graph in (A)

Step-by-step explanation:

Negative discriminant of a quadratic function implies the corresponding quadratic equation ax^2+bx+c=0 does not have any real solutions (it still has solutions in the complex domain, however). Graphically, this corresponds to a parabola that never intersects the x axis for any value x, i.e. it lies either fully above or fully below the x axis. This situation is depicted in the case (A), where the parabola lies below the x axis and has no x-intercepts.

The cases (B), (C), and (D) all intersect the x axis in at least one point.

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."

yes

step-by-step explanation:

yes