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Polynomial Inequalities

Polynomial Inequalities: Level 2 Challenges


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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