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senthamil paavai

· started a discussion

· 1 Months ago

Why alpha+beta is -b? (Question: 112219.0 )

alpha + beta should be +b as per question. Why it is taken as -b?

Question:
If \(\alpha,\beta\) are roots of x2 + bx+c =0, then \(\alpha\beta^2+\alpha^2\beta+\alpha\beta\) is equal to:
Options:
A) c (1-b)
B) 0
C) -bc
D) None of these
Solution:
Ans: (a)

Using the sum and product of roots formulae, we'll get

Here α + β = -b, αβ = c

∴ αβ2 + α2β + αβ = αβ (β + α) + αβ

= c (-b) + c

= -bc + c = c (1-b)

Knowledge Expert

· commented

· 1 Months ago

Here α + β = -b, αβ = c ∴ αβ2 + α2β + αβ = αβ (β + α) + αβ = c (-b) + c = -bc + c = c (1-b)
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