# 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 )= x

^{3}- ( α + β + γ ) x^{2}+ (αβ + βγ + γα ) x^{ }- (αβγ) ...........................(1)given function f(x) = x

^{3 }- β x^{2 }- (α/2) x - γ .............................. (2)By comparing coefficients of x

^{2}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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