Polynomials

Hong Kong

Stage 4 - Stage 5

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`)=4`x`2−8`x`+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`)=4`x`3−`x`2+7`x`+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`)=2`x`3−8`x`2+6`x`+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

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