Product of real roots of the equation $t^{2}x^{2}+|x|+9=0$
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is always positve
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is always negative
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does not exists
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none of these
Reveal answer
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C
Correct answer
Explanation
For real x, t^2x^2 is nonnegative and |x| is nonnegative, while 9 is positive. Therefore the expression cannot equal zero, so there are no real roots and their product does not exist.
AI explanation
Because t squared is always positive or zero and the constant 9 is positive, the first term of the equation is non-negative. The middle term, the absolute value of x, is also non-negative. The sum of two non-negative terms and the positive number 9 can never equal zero, meaning the equation has no real solutions. Therefore, the roots of the equation do not exist, so their product does not exist.