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If alpha and beta are the zeroes of the polynomial 2x^2+7x+5, then value of alpha+beta+alpha*beta |
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Answer» Step-by-step EXPLANATION: give th root of equation 2x 2 −7x+5=0 are \alpha ,\betaα,β Compare it with: ax^2+bx+c=0ax 2 +bx+c=0 So: a=2 ,b=-7 and c=5 We KNOW that: \alpha+\beta=-b/aα+β=−b/a =7/2...............(1) \alpha*\beta=c/aα∗β=c/a =5/2.............(2) Given \FRAC{\alpha^2}{\beta}+\frac{\beta^2}{\alpha} β α 2
+ α β 2
\implies \frac{\alpha^3+\beta^3}{\alpha*\beta}⟹ α∗β α 3 +β 3
\implies \frac{(\alpha+\beta)(\alpha^2-\alpha*\beta+\beta^2)}{\alpha*\beta}⟹ α∗β (α+β)(α 2 −α∗β+β 2 )
\implies \frac{(\alpha+\beta)([\alpha+\beta]^2-3\alpha*\beta)}{\alpha*\beta}⟹ α∗β (α+β)([α+β] 2 −3α∗β)
From 1 and 2 \implies \frac{(7/2)(49/4-3*5/2)}{5/2}⟹ 5/2 (7/2)(49/4−3∗5/2)
\implies \frac{(7/2)(19/4)}{5/2}⟹ 5/2 (7/2)(19/4)
\implies \frac{133/8}{5/2}⟹ 5/2 133/8
\implies 133/8*2/5⟹133/8∗2/5 \implies 133/20⟹133/20 The answer is 133/20 |
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