Question
Download Solution PDFयदि k समीकरण x(x + 1) + 1 = 0 के मूलों में से एक है तो इसका दूसरा मूल क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
द्विघात समीकरण ax2 + bx + c = 0 के लिए
मूलों का योग =
मूलों का गुणनफल =
गणना:
माना दूसरा मूल β है
दिया गया समीकरण x(x + 1) + 1 = 0 है
⇒ x2 + x + 1 = 0
a = 1, b = 1 और c = 1
चूँकि k समीकरण का मूल है
⇒ k2 + k + 1 = 0
⇒ k2 = -k - 1 ..(i)
मूलों का योग =
⇒ β + k = -1
⇒ β = -1 - k .....(ii)
समीकरण (i) और (ii) से, हम प्राप्त करते हैं
⇒ β = k2
∴ दूसरा मूल = k2
दिया गया समीकरण x(x + 1) + 1 = 0 है
अब (x2 + x + 1) = 0 का गुणनखंड
⇒ x = ω या ω2
माना k = ω
∴ दूसरा मूल = ω2 = k2
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