Question

find the condition that the zeros of polynomial f(x)=x³-px²+qx-r may be in arithmetic progression​

Answer 1

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for them to be in ap:

let the zeroes be

a-d,a,a+d

sum of zeroes=

a-d+a+a+d=-(-p)

3a=p

a=p/3

therefore one of the zeroes must p/3

Answer 2

Answer:

important formulas :-

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☆ A n = A + (n - 1) d .

☆ Sn = n/2[ 2a + ( n - 1 ) d ] .

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Answer :-

☆ let the zeroes be

:- a-d,a,a+d

a-d,a,a+dsum of zeroes=

:- a-d+a+a+d=-(-p)

=> 3a=p

=> a=p/3

therefore one of the zeroes must p/3