(C) Given the equation ${t^2}{x^2} + |x| + 9 = 0$. For any real number $t$ and $x$,we know that ${t^2}{x^2} \ge 0$ and $|x| \ge 0$. Therefore,${t^2}{x

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(C) Given the equation ${t^2}{x^2} + |x| + 9 = 0$. For any real number $t$ and $x$,we know that ${t^2}{x^2} \ge 0$ and $|x| \ge 0$. Therefore,${t^2}{x^2} + |x| + 9 \ge 9$. Since the expression is always greater than or equal to $9$,it can never be equal to $0$. Thus,the equation has no real roots. Consequently,the product of the real roots does not exist.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

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What is the product of the real roots of the equation ${t^2}{x^2} + |x| + 9 = 0$?

AIEEE 2002 All AIEEE

A
Is always positive
B
Is always negative
C
Does not exist
D
None of these

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4-2.Quadratic Equations and Inequations

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Solution of quadratic equations and Nature of roots

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What is the product of the real roots of the equation ${t^2}{x^2} + |x| + 9 = 0$?

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