The quadratic equation whose roots are a, 1 a is: - Vidyadip

MCQ

The quadratic equation whose roots are $a, \frac{1}{a}$ is:

✓
$a x^2-\left(a^2+1\right) x+a=0$
B
$a x^2-\left(a^2-1\right) x+a=0$
C
$a x^2-\left(a^2-1\right) x-a=0$
D
none of the above

✓

Answer

Correct option: A.

$a x^2-\left(a^2+1\right) x+a=0$

(a) $a x^2-\left(a^2+1\right) x+a=0$
Explanation:
Quadratic equation whose roots are $a, \frac{1}{a}$ be
$\begin{array}{l}x^2-\left(a+\frac{1}{a}\right) x+1=0 \\ \Rightarrow x^2-\left(\frac{a^2+1}{a}\right) x+1=0 \\ \Rightarrow a x^2-\left(a^2+1\right) x+a=0\end{array}$

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