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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 $x$ ?

\frac{1}{4}

1

4

\frac{9}{4}

by Anish Harsha

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

(-2,4)

[4,6]

(-2,6)

(4,6)

by Sandeep Bhardwaj

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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?

c = 0 Can't be determined c > 0 c < 0

by Priyansh Sangule

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

by Sandeep Bhardwaj

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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 $x=1$ .

-1<x<2

-2<x<1

-1<x<1

-2<x<2

by Kumar Gupta

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