Polynomial Inequality Coefficient Change

Question

An engineering stress test is modeled by the polynomial inequality $$x^3-4*x^2+x+6>0$$, where $$x$$ represents the applied load. If the coefficient of $$x^2$$ is halved, the model changes to the inequality $$x^3-2*x^2+x+6>0$$. How is the solution set for $$x$$ affected by this modification?

Accepted Answer

The solution becomes a single continuous interval for $$x > -1.23$$ approximately, including a wider range of loads.

Answer

The solution remains as two disjoint intervals, one at low loads and one at high loads.

Answer

The solution becomes restricted to loads between 1 and 3.

Answer

No solution exists since the polynomial becomes always positive.

Polynomial Inequality Coefficient Change

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