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3.06 Roots and zeros

Interactive practice questions

Consider the function $f\left(x\right)=x^4-7x^3+12x^2+4x-16$f(x)=x47x3+12x2+4x16.

a

Is $5$5 a zero of the function?

Yes

A

No

B
b

Is $4$4 a zero of the function?

Yes

A

No

B
c

Is $-1$1 a zero of the function?

Yes

A

No

B
Easy
1min

Consider the function $f\left(x\right)=\left(x+1\right)^2\left(x-6\right)\left(x+2\right)^5$f(x)=(x+1)2(x6)(x+2)5.

Easy
1min

Consider the function $f\left(x\right)=-3\left(x-6\right)^4\left(x+2\right)^5x^3$f(x)=3(x6)4(x+2)5x3.

Easy
1min

Consider the function $f\left(x\right)=x^3-3x^2-5x+15$f(x)=x33x25x+15.

Easy
3min
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Outcomes

III.N.CN.9

Know the fundamental theorem of algebra; show that it is true for quadratic polynomials.

III.A.APR.3

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

III.F.IF.7.c

Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

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