Graph minus!

Since P is graphed, I assume it is real, and so are a, b, c, d. A polynomial P(x) = x^4 + ax^3 + bx^2 + cx + d can also be expressed as P(x)=(x-s)(x-t)(x-u)(x-v). The intersections with the x-axis give the real zeros which we will say are at x=s and x=t.

Values are read from the graph, so I try to provide readings with estimated uncertainties.

• The product of the zeroes is $stuv=d=P(0)=5.4 \pm 0.2$
• The sum of the real zeroes is $s+t=1.7 + 3.8 = 5.5 \pm 0.1$
• The product of the nonreal zeroes is $uv=stuv/st=5.4/(1.7×3.8)$ , so $uv=0.8 \pm 0.2$
• The sum of coefficients is $1+a+b+c+d=P(1)=3.3 \pm 0.2$
• We have $P(-1)=4.3 \pm 0.2$

In the graph, the y-intercept is $5$ , meaning the product of all roots is $5$ . The real roots are around $1.7$ and $3.9$ , whose sum is greater than $5$ . $P(-1)=4$ . Because all the coefficients are positive, and $d=5$ , the sum of coefficients exceeds $5$ . The product of complex roots is $\frac{5)}{1.7*3.9}$ = 0.754), which is the smallest value. As a result, $A$ is the answer.