यदि \(\sqrt{2}\) और \(\sqrt{3}\) किसी द्विघात बहुपद के शून्यक हैं, तो उस बहुपद के गुणांक किस प्रकार होंगे?
If \(\sqrt{2}\) and \(\sqrt{3}\) are zeroes of a quadratic polynomial, what type of coefficients will that polynomial have?
Explanation opens after your attempt
B. कम से कम एक गुणांक अपरिमेय होगाAt least one coefficient will be irrational
Concept
The sum \(\sqrt{2}+\sqrt{3}\) is irrational, so the coefficient of (x) in the monic polynomial is irrational. For rational coefficients, such zeroes must occur as conjugates.
Why this answer is correct
The correct answer is B. कम से कम एक गुणांक अपरिमेय होगा / At least one coefficient will be irrational. The sum \(\sqrt{2}+\sqrt{3}\) is irrational, so the coefficient of (x) in the monic polynomial is irrational. For rational coefficients, such zeroes must occur as conjugates.
Exam Tip
योग \(\sqrt{2}+\sqrt{3}\) अपरिमेय है, इसलिए एकक बहुपद में (x) का गुणांक अपरिमेय होगा। परिमेय गुणांक के लिए ऐसे शून्यक संयुग्मी रूप में होने चाहिए।
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