Find the polynomial whose zeroes are 1,2,5
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Answer:
the polynomial is x^3-8x^2+17x-10
Step-by-step explanation:
let,
first zero = 1 (alfa)
second zero = 2 (beta)
third zero = 5 (gamma)
Now,
sum of zeroes (alfa+beta+gamma) = 1+2+5
=8x
sum of zeroes two at a time (alfa*beta+beta*gamma+gamma*alfa)=2+10+5
=17
product of zeroes (alfa*beta*gamma)=1*2*5
=10
now,
p(x)=k(x^3-(alfa+beta+gamma)x^2+(alfa*beta+beta*gamma+gamma*alfa)x-(alfa*beta*gamma)
=>k(x^3-(8)x^2+17x-10)
=>k(x^3-8x+17x-10)
put k= 1
therefore p(x) = x^3-8x+17x-10
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