Waste less time on Facebook — follow Brilliant.
Already have an account? Log in here.
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.
\[\large (n^2-2)(n^2-20)<0\]
How many integers \(n\) satisfy the inequality above?
Already have an account? Log in here.
by
Piyush Maheshwari
Over the ranges
\[ \begin{eqnarray} -1 \leq & v & \leq 1 \\ -2 \leq & u & \leq -0.5 \\ -2 \leq & z & \leq -0.5 \\ \end{eqnarray} \]
what is the range of \(w = \frac {vz}{u} \)?
Already have an account? Log in here.
by
Sanjeet Raria
If \(x\) is an integer that satisfies the inequality
\[ 9 < x ^2 < 99 \]
find the difference between the maximum and minimum possible values of \(x.\)
Already have an account? Log in here.
by
Chung Kevin
As \(x\) and \(y\) ranges over all real values, what is the minimum value of
\[ (15x + 30y + 20)^2 + (20x + 40y + 15)^2? \]
Already have an account? Log in here.
by
Calvin Lin
Considering \(y=\dfrac{2x}{1+x^{2}}\), where \(x\) and \(y\) are real numbers, what is the range of the expression \(y^{2}+y-2\)?
Already have an account? Log in here.
by
Sandeep Bhardwaj