निम्न द्विघात समीकरणों के मूलों की प्रकृति ज्ञात कीजिए। यदि मूलों का आस्तित्व हो तो उन्हें ज्ञात कीजिए:
$3 straight x squared space minus space 4 square root of 3 straight x space plus space 4 space equals space 0$

Solution

$3 straight x squared space minus space 4 square root of 3 straight x space plus space 4 space equals space 0$
यहाँ, $straight a space equals space 3 comma space space straight b space equals space minus space 4 square root of 3 comma space space straight c space equals space 4$
$straight D space equals space straight b squared space minus space 4 ac equals space open parentheses space minus space 4 square root of 3 space close parentheses squared space minus space 4 space left parenthesis space 3 space right parenthesis space left parenthesis space 4 space right parenthesis equals space 48 space minus space 48 space equals space 0$
चूँकि, D = 0
अत: दिए गए समीकरण के दो समान मूल हैं।
$straight x space equals space fraction numerator negative space straight b space plus-or-minus space square root of straight D over denominator 2 straight a end fraction space equals space fraction numerator negative space left parenthesis space minus space square root of 3 space right parenthesis space plus-or-minus space square root of 0 over denominator 2 space left parenthesis space 3 space right parenthesis end fraction$
$equals space fraction numerator 4 space square root of 3 over denominator 6 end fraction space equals space fraction numerator 2 space square root of 3 over denominator 3 end fraction space equals space fraction numerator 2 over denominator square root of 3 end fraction$
अत: मूल हैं $fraction numerator 2 over denominator square root of 3 end fraction comma space space fraction numerator 2 over denominator square root of 3 end fraction$