Question

The zeros of the function f(x) = (x + 2)^2 - 25 are

(1) -2 and 5 (3) -5 and 2
(2) -3 and 7 (4) -7 and 3

Answer 1

f(x) = 0

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1)

İf x=-2,


`f(-2) = ((-2) + 2 ) ^(2) -25 = 0-25 = -25`

f(x) ≠ 0

If x= 5


`f(5) = (5+2)^(2) - 25 = 49 - 25 = 24`

f(x) ≠ 0
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2)

If x= -3


`f(-3) = ((-3) + 2) ^(2) - 25 = 1 -25 =-24`

f(x) ≠ 0

If x= 7


`f(7) = (7+2)^(2) - 25 = 81 - 25 = 56`

f(x) ≠ 0

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3)

If x= -5


`f(-5) = ((-5)+2)^(2) - 25 = 9-25 = -16`

f(x) ≠ 0

If x= 2


`f(2) = (2+2)^(2) - 25 = 16-25 = -9`

f(x) ≠ 0
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4)

If x= -7


`f(-7) = ((-7) +2 )^(2) - 25 = 25-25 =0`


`f(x) =0` ✔

If x= 3


`f(3) = (3+2)^(2) - 25 = 25-25 =0`


`f(x) =0` ✔

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Answer: 4

Answer 2

`The\ zeros\ of\ a\ function\ f(x)\ is\ when\ f(x)=0.\\------------------------\\f(x)=(x+2)^2-25\\the\ zeros,\ if\ f(x)=0\iff(x+2)^2-25=0\\\\(x+2)^2-5^2=0\ \ \ \ |use\ a^2-b^2=(a-b)(a+b)\\\\(x+2-5)(x+2+5)=0\\\\(x-3)(x+7)=0\iff x-3=0\ or\ x+7=0\\\\x-3=0\ \ \ |add\ 3\ to\ both\ sides\\\boxed{x=3}\\or\\x+7=0\ \ \ \ \ |subtract\ 7\ from\ both\ sides\\\boxed{x=-7}\\\\Answer:\boxed{(4)\ -7\ and\ 3}`