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Choose the correct answer from the given four options in the following questions:
The quadratic equation $ 2 x^{2}-\sqrt{5} x+1=0 $ has
(A) two distinct real roots
(B) two equal real roots
(C) no real roots
(D) more than 2 real roots
To do:
We have to find the correct answer.
Solution:
$2 x^{2}-\sqrt{5} x+1=0$
Comparing with $a x^{2}+b x+c=0$, we get,
$a=2, b=-\sqrt{5}$ and $c=1$
Therefore,
$D =b^{2}-4 a c$
$=(-\sqrt{5})^{2}-4 \times(2) \times(1)$
$=5-8$
$=-3<0$
The discriminant is negative.
This implies, the quadratic equation $2 x^{2}-\sqrt{5} x+1=0$ has no real roots.
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