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What is the discriminant \(D\) of the equation \(2x^2+5x+2=0\)?समीकरण \(2x^2+5x+2=0\) का विविक्तकर \(D\) क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 99
For a quadratic equation \(ax^2+bx+c=0\), the discriminant is \(D=b^2-4ac\). Here, \(a=2, b=5, c=2\), so \(D=5^2-4(2)(2)=25-16=9\). Therefore, the correct answer is 9. Since \(D>0\), the equation has two distinct real roots. In exams, carefully retain the minus sign in \(b^2-4ac\); using a plus sign would incorrectly give 41.द्विघात समीकरण \(ax^2+bx+c=0\) के लिए विविक्तकर \(D=b^2-4ac\) होता है। यहाँ \(a=2, b=5, c=2\), इसलिए \(D=5^2-4(2)(2)=25-16=9\)। अतः सही उत्तर 9 है। \(D>0\) होने से इसके दो भिन्न वास्तविक मूल होंगे। परीक्षा में चिन्हों पर विशेष ध्यान दें; \(-4ac\) को गलती से \(+4ac\) न लें।
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