यदि \(x=\sqrt{2}\) बहुपद \(ax^2+bx+c\) का शून्यक है और (a,b,c) परिमेय हैं, तो कौन सा निष्कर्ष सही नहीं हो सकता?
If \(x=\sqrt{2}\) is a zero of \(ax^2+bx+c\) and (a,b,c) are rational, which conclusion cannot be correct?
Explanation opens after your attempt
C. सिर्फ \(\sqrt{2}\) ही अकेला अपरिमेय शून्यक हो और गुणांक परिमेय रहेंOnly \(\sqrt{2}\) is the sole irrational zero while coefficients stay rational
Concept
In a quadratic with rational coefficients an irrational zero comes with its conjugate. In exams be suspicious of a lone irrational root.
Why this answer is correct
The correct answer is C. सिर्फ \(\sqrt{2}\) ही अकेला अपरिमेय शून्यक हो और गुणांक परिमेय रहें / Only \(\sqrt{2}\) is the sole irrational zero while coefficients stay rational. In a quadratic with rational coefficients an irrational zero comes with its conjugate. In exams be suspicious of a lone irrational root.
Exam Tip
परिमेय गुणांकों वाले द्विघात में अपरिमेय शून्यक अपने संयुग्मी के साथ आता है। परीक्षा में अकेले अपरिमेय मूल पर संदेह करें।
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