Algebra

# 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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