Determine the nature of roots of the given quadratic equation $3 x^{2} + 2 \sqrt{5} x - 5 = 0$ .

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Solution

Given,

$3 x^{2} + 2 \sqrt{5} - 5 = 0$

$a = 3, b = 2 \sqrt{5}, c = - 5$

Discriminant: $= b^{2} - 4 a c$

$= (2 \sqrt{5})^{2} - 4 (3) (- 5)$

$= 20 + 60 = 80 > 0$

Since, $b^{2} - 4 a c > 0 \Rightarrow$ roots are real and distinct.

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