Asked by LOL
Which of the following equations has exactly the same solutions as (x−7)(x+9)=0
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Answered by
GPT-5 mini
AI
The given equation factors to zeros x = 7 or x = −9, so its solution set is {7, −9}.
An equivalent polynomial form is
x^2 + 2x − 63 = 0,
since (x − 7)(x + 9) = x^2 + 2x − 63. Other equations with exactly the same solutions include any equation that is algebraically equivalent, e.g.
- x^2 + 2x = 63,
- 2(x − 7)(x + 9) = 0,
- 2x^2 + 4x − 126 = 0,
or any equation whose set of roots is {7, −9} (for example (x − 7)^2(x + 9) = 0 also has the same solution set).
An equivalent polynomial form is
x^2 + 2x − 63 = 0,
since (x − 7)(x + 9) = x^2 + 2x − 63. Other equations with exactly the same solutions include any equation that is algebraically equivalent, e.g.
- x^2 + 2x = 63,
- 2(x − 7)(x + 9) = 0,
- 2x^2 + 4x − 126 = 0,
or any equation whose set of roots is {7, −9} (for example (x − 7)^2(x + 9) = 0 also has the same solution set).
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