Question

45. Discuss nature of roots of
$2x {}^{2} - \sqrt{5} x + 1 = 0$
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Answer 1

$\bold \red \star \: \large \underline{Given:-}$

$2 {x}^{2} - \sqrt{5} x + 1 = 0.$

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$\\ \\ \bold \red \star \: \large \underline{Solution:-}$

We have,

$equation \: \: \: \: 2 {x}^{2} - \sqrt{5} x + 1 = 0.$

Comparing with general equation,

$\: \: \: \: \: \: a {x}^{2} + bx + c = 0.$

Where,

$\: \: \: \: \: \: a = 2 \: \: \: \: \: \: b = - \sqrt{5} \: \: \: \: \: c = 1.$

$\: \: \: \: \: D= {b}^{2} - 4ac. \\ \\ \: \: \: \: \: \: \: \: \: \: = { ( - \sqrt{5}) }^{2} - 4 \times 2 \times 1. \\ \\ \: \: \: \: \: \: \: \: \: \: = 5 - 8. \\ \\ \: \: \: \: \: \: \: \: \: \: = - 3.$

$D < 0.$

Discriminant smaller than zero.

$So, \bold{ \: this \: given \: equation \: has \: \pink{ no \: real \: root}. }$