2023 SSMO Relay Round 2 Problems/Problem 1

Problem

Consider the cubic polynomial $P(x)=ax^3+bx^2+cx+d$ , where $a,b,c,d$ are single-digit integers, which has roots of approximately $x \approx -0.9518399, 0.2055095, 1.460616.$ Compute $|f(3)|$ .

Solution

Note that the sum of the three roots is approximately $0.71\approx\frac{5}{7}$ . So, we have $a=7$ . Therefore $|f(3)| \approx 7(3-(-0.95))(3-0.2)(3-1.46)\approx\boxed{119}.$

~pinkpig

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2023 SSMO Relay Round 2 Problems/Problem 1

Problem

Solution