Question

if a b c are zeroes of the polynomial x3-4x+1, then a3+b3+c3 =?

Answer 1

$\red{Answer}$

For a cubic polynomial

Sum of roots : -b/a

Product of roots :- -d/a

sum of product of roots taken 2 at a time :- c/a

here a=1,b=0,c=-4,d=1

so a+b+c=-b/a=0

and abc=-d/a=-1

Now we know

(a+b+c)³=a³+b³+c³+3abc(a+b+c)

now substitute a+b+c=0 and abc=-1

(0)³=a³+b³+c³+3(-1)(0)

a³+b³+c³=0

$\pink{Value \ is \ 0}$

hope it helps

$\green{Peace}$

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