If ' $a$ ' is a rational number, then the roots of the equation $x^2-3 a x+a^2-2 a-4=0$ are

If ' $a$ ' is a rational number, then the roots of the equation $x^2-3 a x+a^2-2 a-4=0$ are
  1. rational and equal numbers
  2. different real numbers
  3. different rational numbers only
  4. not real numbers

Solution

$\begin{gathered} x^2-3 a x+a^2-2 a-4=0 \\ \mathrm{D}=9 a^2-4 a^2+8 a+16=5 a^2+8 a+16\gt0 \end{gathered}$
So, roots are real and distinct.

Asked in: AP EAMCET 2024 (22 May Shift 2)

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