Question

Find the polynomial whose zeroes are 1,2,5

Answer 1

$x - 1 \\ 2x - 4 \\ {x}^{2} - 25$

Answer 2

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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