APFIVE Polynomial Inequality Coefficient Change
In an engineering experiment, a stress test is modeled by the polynomial inequality $$x^3-4*x^2+x+6>0$$, where $$x$$ represents the applied load. What would happen if the coefficient of $$x^2$$ is halved, changing the inequality to $$x^3-2*x^2+x+6>0$$; how does the solution set for $$x$$ change?
A
No solution exists since the polynomial becomes always positive.
B
The solution remains as two disjoint intervals, one at low loads and one at high loads.
C
The solution becomes a single continuous interval for $$x > -1.23$$ approximately, including a wider range of loads.
D
The solution becomes restricted to loads between 1 and 3.
Question Leaderboard
Not enough data yet to show leaderboard.