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Polynomial Inequalities

When does revenue exceed cost? When will one race car pass another? Model these values with polynomials and use polynomial inequalities to solve questions like these and more.

Level 2

         

Let \(x\) be a real number such that the square root of \(x\) is greater than the square of \(x\). Which of the following is a possible value of \(x\)?

Find the interval of \(v\) which satisfies the inequality \[(v+2)^2(v-4)(v-6)<0.\]

Consider the polynomial \( p(x) = ax^2 + bx + c \) has no real roots. Provided that \(25a+5b+c>0\), which of the following condition must be true?

How many integer values of \(u\) satisfy \[u^4+u^3-12u^2<0?\]

The graph above is a quadratic function, \(y =x^2+kx-2\) for some constant \(k\). What is the solution to the quadratic inequality \(x^2 + kx-2 < 0 \)?

Clarification: The graph intersects the \(x\)-axis at \(x=1\).

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