Intermediate Value Theorem
Interactive practice questions
Suppose we have a polynomial $P\left(x\right)$P(x) such that $P\left(-6\right)=1$P(−6)=1 and $P\left(-5\right)=6$P(−5)=6. What conclusion can we make using the intermediate value theorem?
We cannot conclude anything about the zeros of $P\left(x\right)$P(x).
There is exactly one real zero between $x=-6$x=−6 and $x=-5$x=−5.
There is at least one real zero between $x=-6$x=−6 and $x=-5$x=−5.
There is no real zero between $x=-6$x=−6 and $x=-5$x=−5.
Consider the polynomial $P\left(x\right)=4x^2-8x+2$P(x)=4x2−8x+2. Dylan would like to know if it has a real zero between $x=1$x=1 and $x=2$x=2.
Consider the polynomial $P\left(x\right)=4x^3-x^2+7x+7$P(x)=4x3−x2+7x+7. Sharon would like to know if it has a real zero between $x=-0.8$x=−0.8 and $x=-0.7$x=−0.7.
Consider the polynomial $P\left(x\right)=2x^3-8x^2+6x+6$P(x)=2x3−8x2+6x+6. Yuri would like to know if it has a real zero between $x=2.5$x=2.5 and $x=2.6$x=2.6.