Algebra III - 5.7 - Roots and Zeros

Solve the equation.  $x^2-3x-10=0$  (Select all that apply)

• -2

• 5

• 2

• -5

State the number and type of roots.  $x^2-3x-10=0$  

• 2 real roots

• 5 real roots

• 2 real roots, 1 imaginary root

• 3 imaginary roots

Solve the equation.  $0=x^3-8$  

•  $2$  

•  $-1+i\sqrt{3}$  

•  $-1-i\sqrt{3}$  

•  $-2$  

State the possible number of positive real zeros, negative real zeros, and imaginary zeros of the function.  $f\left(x\right)=x^3-2x^2+2x-6$  

• 3 or 1 Positive; 0 Negative; 0 or 2 Imaginary

• 1 or 3 Positive; 0 or 2 Negative; 0,2, or 4 Imaginary

• 0 Positive; 0 or 2 Negative; 2 or 4 Imaginary

• 1 Positive; 1 or 3 Negative; 0 or 2 Imaginary

Find all the zeros of the function.  $f\left(x\right)=x^3+9x^2+6x-16$  

• -8

• 8

• -2

• 1

Find all the zeros of the function.  $f\left(x\right)=x^3+7x^2+4x+28$  

• -7

• 7

•  $-2i$  

•  $2i$  

Find all the zeros of the function.  $f\left(x\right)=x^4-6x^3+9x^2+6x-10$  

•  $-1$  

•  $1$  

•  $3-i$  

•  $3+i$  

State the number and type of roots.  $0=x^3-8$  

• 1 real, 2 imaginary

• 2 real; 1 imaginary

• 3 real

• 3 imaginary

Solve the equation.  $x^3+12x^2+32x=0$  

• -8

• 8

• -4

• 0

Write a polynomial function of least degree with integral coefficients that have the given zeros: 4, -1, 6

• $f\left(x\right)=x^3-9x^2+14x+24$

• $f\left(x\right)=x^4-5x^3+5x^2+5x-6$

• $f\left(x\right)=x^4-3x^3-x^2-27x-90$

• $f\left(x\right)=x^3-4x^2-15x+68$