Question
Download Solution PDFयदि n समीकरण x2 + px + m = 0 का एक मूल है और m समीकरण x2 + px + n = 0 का एक मूल है, जहाँ m ≠ n है, तो p + m + n का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
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दिया गया है,
n समीकरण x2 + px + m = 0 का मूल है
⇒ \(n^2 + pn + m = 0\) ..... (1)
साथ ही, m समीकरण x2 + px + n = 0 का मूल है
⇒ \(m^2 +pm+ n =0\) ..... (2)
अब समीकरण (1) - समीकरण (2), हमें प्राप्त होता है
⇒ \((n^2 – m^2) + p(n – m) – (n – m) = 0\)
⇒ \((n – m) [(n + m) + p – 1] = 0\)
⇒ \(n + m + p – 1 = 0\) ..... ( n ≠ m)
⇒ n + m + p = 1
∴ विकल्प (c) सही है।
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