Question
Download Solution PDFयदि α और β द्विघात बहुपद f (x) = x2 - 5x +6 के शून्यक हैं तो ( α2β + β2α ) का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
α और β समीकरण ax2 + bx + c =0 के मूल हैं,
मूलों का योग (α + β) = \(\rm \frac{-b}{a}\)
मूलों का गुणनफल (αβ) = \(\rm \frac{c}{a}\)
(x + y)2 = x2 + y2 + 2xy
गणना:
दिया गया: f (x) = x2 - 5x + 6
ax2 + bx + c =0 के साथ f (x) की तुलना करके हमारे पास a = 1, b = -5 और c = 6 हैं।
अब, मूलों का योग = α + β = \(\rm \frac{-b}{a}\) = \(\rm \frac{-(-5)}{1}\) = 5
और मूलों का गुणनफल αβ = \(\rm \frac{c}{a}\) = \(\rm \frac{6}{1}\) = 6।
अब, α2β + β2α = αβ ( α+ β )
= 6 × 5
= 30
सही विकल्प 2 है।
Last updated on Jun 20, 2025
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