Which of the following is/are always false?

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(C) For a quadratic equation $ax^2 + bx + c = 0$ with irrational coefficients, the roots are not necessarily irrational in pairs. For example, conside

Vedclass · Accepted Answer

$A$ quadratic equation with irrational coefficients has zero or two irrational roots

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(C) For a quadratic equation $ax^2 + bx + c = 0$ with irrational coefficients, the roots are not necessarily irrational in pairs. For example, consider the equation $x^2 - (1 + \sqrt{2})x + \sqrt{2} = 0$. The roots are $x = 1$ and $x = \sqrt{2}$. Here, one root is rational and one is irrational. Thus, the statement that such an equation must have zero or two irrational roots is false. Therefore, option $C$ is always false.

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