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
- rational and equal numbers
- different real numbers
- different rational numbers only
- 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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