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50 POINTS ASAP BRAINLIEST

State how many imaginary and real zeros the function has.

f(x) = x^3 + 5x^2 + x + 5

0 imaginary; 3 real
1 imaginary; 2 real
3 imaginary; 0 real
2 imaginary; 1 real

Respuesta :

wegnerkolmp2741o

Answer:

1 real root   2 imaginary roots

Step-by-step explanation:

f(x) = x^3 + 5x^2 + x + 5

Set equal to zero to find the zeros

0  = x^3 + 5x^2 + x + 5

Factor by grouping

0 = x^2( x+5)  + 1( x+5)

0 = (x+5) ( x^2+1)

Using the zero product property

x+5 =0    x^2+1 =0

x=-5    x^2 = -1

x=-5    x = ±i

1 real root   2 imaginary roots

Helpmeplzmy

Answer:

1 real root   2 imaginary roots

Step-by-step explanation:

f(x) = x^3 + 5x^2 + x + 5

Set equal to zero to find the zeros

0  = x^3 + 5x^2 + x + 5

Factor by grouping

0 = x^2( x+5)  + 1( x+5)

0 = (x+5) ( x^2+1)

Using the zero product property

x+5 =0    x^2+1 =0

x=-5    x^2 = -1

x=-5    x = ±i

1 real root   2 imaginary roots

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