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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

A2.NQ.B.7

Know and apply the Fundamental Theorem of Algebra.

A2.APR.A.5

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to sketch the function defined by the polynomial.

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