Polynomial Inequalities

Polynomial Inequalities: Level 2 Challenges


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

Find the interval of vv which satisfies the inequality (v+2)2(v4)(v6)<0.(v+2)^2(v-4)(v-6)<0.

Consider the polynomial p(x)=ax2+bx+c p(x) = ax^2 + bx + c has no real roots. Provided that 25a+5b+c>025a+5b+c>0, which of the following condition must be true?

How many integer values of uu satisfy u4+u312u2<0?u^4+u^3-12u^2<0?

The graph above is a quadratic function, y=x2+kx2y =x^2+kx-2 for some constant kk. What is the solution to the quadratic inequality x2+kx2<0x^2 + kx-2 < 0 ?

Clarification: The graph intersects the xx-axis at x=1x=1.


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