Hong Kong
Stage 4 - Stage 5

# 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).

A

There is exactly one real zero between $x=-6$x=6 and $x=-5$x=5.

B

There is at least one real zero between $x=-6$x=6 and $x=-5$x=5.

C

There is no real zero between $x=-6$x=6 and $x=-5$x=5.

D
Easy
1min

Consider the polynomial $P\left(x\right)=4x^2-8x+2$P(x)=4x28x+2. Dylan would like to know if it has a real zero between $x=1$x=1 and $x=2$x=2.

Easy
1min

Consider the polynomial $P\left(x\right)=4x^3-x^2+7x+7$P(x)=4x3x2+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.

Easy
4min

Consider the polynomial $P\left(x\right)=2x^3-8x^2+6x+6$P(x)=2x38x2+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.

Easy
2min