What are the zeros of the function f(x)=x^2+5x+5 written in simplest radical form?

parheliubdr

parheliubdr

Answered question

2023-02-24

What are the zeros of the function f ( x ) = x 2 + 5 x + 5 written in simplest radical form?

Answer & Explanation

Bruno Stanley

Bruno Stanley

Beginner2023-02-25Added 7 answers

We have:
f ( x ) = x 2 + 5 x + 5
Method 1 - Completing the square
Solve:
0 = 4 f ( x )
0 = 4 ( x 2 + 5 x + 5 )
0 = 4 x 2 + 20 x + 20
0 = ( 2 x ) 2 + 2 ( 2 x ) ( 5 ) + 25 - 5
0 = ( 2 x + 5 ) 2 - ( 5 ) 2
0 = ( ( 2 x + 5 ) - 5 ) ( ( 2 x + 5 ) + 5 )
0 = ( 2 x + 5 - 5 ) ( 2 x + 5 + 5 )
Then:
2 x = - 5 ± 5
Dividing both sides by 2, we find:
x = - 5 2 ± 5 2
Addison Stuart

Addison Stuart

Beginner2023-02-26Added 5 answers

Method 2 - Quadratic formula
Note that f(x) is in standard quadratic form:
f ( x ) = a x 2 + b x + c
with a=1, b=5 and c=5.
According to the quadratic formula, this has zeros:
x = - b ± b 2 - 4 a c 2 a
x = - ( 5 ) ± ( 5 ) 2 - 4 ( 1 ) ( 5 ) 2 ( 1 )
x = - 5 ± 25 - 20 2
x = - 5 ± 5 2
x = - 5 2 ± 5 2

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