Question
Download Solution PDFα మరియు β అనేవి వర్గ బహుపది f (x) = x2 - 5x +6, యొక్క సున్నాలు అయితే, ( α2β + β2α ) విలువను కనుగొనండి.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFకాన్సెప్ట్:
α మరియు β సమీకరణం యొక్క మూలాలు అయితే, ax2 + bx + c =0
మూలాల మొత్తం (α + β) = \(\rm \frac{-b}{a}\)
మూలాల లబ్దం (αβ) = \(\rm \frac{c}{a}\)
(x + y)2 = x2 + y2 + 2xy .
సాధన:
ఇవ్వబడింది: f (x) = x2 - 5x + 6
f(x)ని ax2 + bx + c =0 తో పోల్చి చూస్తే, మనకు , a = 1 , b= -5 మరియు c= 6 ఉన్నాయి.
ఇప్పుడు, మూలాల మొత్తం= α + β = \(\rm \frac{-b}{a}\) = \(\rm \frac{-(-5)}{1}\) = 5
మరియు మూలాల లబ్దం αβ = \(\rm \frac{c}{a}\) = \(\rm \frac{6}{1}\) = 6 .
ఇప్పుడు, α2β + β2α = αβ ( α+ β )
= 6 × 5
= 30
సరైన ఎంపిక 2.
Last updated on May 31, 2025
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