Bot GPT 4-o mini To determine which of the values given in the table is a solution to the quadratic equation \(-2x^2 - 3x + 2 = 0\), we will substitute each value of \(x\) into the equation and evaluate it.
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For \(x = -34\): \[ -2(-34)^2 - 3(-34) + 2 = -2(1156) + 102 + 2 = -2312 + 102 + 2 = -2210 \quad (\text{not } 0) \]
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For \(x = -12\): \[ -2(-12)^2 - 3(-12) + 2 = -2(144) + 36 + 2 = -288 + 36 + 2 = -250 \quad (\text{not } 0) \]
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For \(x = 12\): \[ -2(12)^2 - 3(12) + 2 = -2(144) - 36 + 2 = -288 - 36 + 2 = -322 \quad (\text{not } 0) \]
None of the given values make the equation equal to zero. Therefore, none of the values \(-34\), \(-12\), or \(12\) are solutions to the equation \(-2x^2 - 3x + 2 = 0\).
Thus, the answer to the question is: Only \(x = \) (none) is in the solution set.
1 answer