α మరియు β అనేవి వర్గ బహుపది f (x) = x2 - 5x +6, యొక్క సున్నాలు అయితే, ( α2β + β2α ) విలువను కనుగొనండి.

  1. 20
  2. 30
  3. 50
  4. 60

Answer (Detailed Solution Below)

Option 2 : 30
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Detailed Solution

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కాన్సెప్ట్:

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​

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