ICSE Class 10 Answered
Please help me in these questions
Asked by bhaveshjshah11 | 05 Dec, 2023, 09:43: AM
Expert Answer
If multiple number of questions are asked in one posting , only first question will be answered.
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f (x) = ( x- α ) ( x - β ) ( x - γ )= x3- ( α + β + γ ) x2 + (αβ + βγ + γα ) x - (αβγ) ...........................(1)
given function f(x) = x3 - β x2 - (α/2) x - γ .............................. (2)
By comparing coefficients of x2 of eqn.(1) and eqn.(2) , we get
( α + β + γ ) = β , hence we get , α + γ = 0 ...............(3)
By comparing coefficients of x of eqn.(1) and eqn.(2) , we get
(αβ + βγ + γα ) = - α/2
β( α + γ ) + γ α = - α/2
Using eqn.(3) , we get from above expression as γ α = - α/2 or γ = -1/2
if γ = -1/2 , then from eqn.(3) , we get α = 1/2
By comparing constant terms of eqn.(1) and eqn.(2) , we get
(αβγ) = γ or α β = 1
if α = 1/2 and (α β) = 1 , then β = 2 .
Then given polynomial is
f(x) = ( x - (1/2) ) ( x - 2 ) ( x + (1/2) )
f(x) = ( 3 - (1/2) ) ( 3 -2 ) ( 3 + (1/2)) = (5/2) (7/2) = 35/4
Answered by Thiyagarajan K | 05 Dec, 2023, 02:49: PM
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