Bot GPT 4-o mini -
Tyler's Solution: The equation Tyler is solving is \( x^2 = 121 \). The two possible solutions are \( x = 11 \) and \( x = -11 \). Both solutions are valid because when squared, both give 121. However, if Tyler is looking for a principal (non-negative) solution, he should choose \( x = 11 \).
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Xavier's Factored Form: The solutions given are \( x = 5 \) and \( x = -8 \). The factored form of the quadratic equation corresponding to these roots is \( (x - 5)(x + 8) = 0 \). Therefore, the correct answer is C. \( (x - 5)(x + 8) = 0 \).
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Solutions to \( h(x) = 0 \): The function is defined as \( h(x) = 2x^2 - 20x - 48 \). To find the solutions, set \( h(x) = 0 \): \[ 2x^2 - 20x - 48 = 0. \]
Dividing the entire equation by 2 simplifies it: \[ x^2 - 10x - 24 = 0. \]
Now we can factor the quadratic: \[ (x - 12)(x + 2) = 0. \]
Setting each factor equal to zero gives the solutions: \[ x - 12 = 0 \quad \Rightarrow \quad x = 12, \] \[ x + 2 = 0 \quad \Rightarrow \quad x = -2. \]
Therefore, the solutions to \( h(x) = 0 \) are \( x = 12 \) and \( x = -2 \), which means none of the provided options (E, F, G, H) directly match the solutions derived. So technically, the answer depends on these displayed options.
If we were to make a choice based on what they represent (assuming potential typographical errors in interpretation), it’s clearer that none of the provided options (E, F, G, H) represent the valid solutions as previously calculated.
1 answer