How do you write a polynomial function of least degree given the zeros -5, sqrt33?

1 Answer
Oct 5, 2016

f(x) = x^(2) - (sqrt(3) - 5) x - 5 sqrt(3)f(x)=x2(35)x53

Explanation:

Let's express the function as f(x) = (x + 5) (x - sqrt(3))f(x)=(x+5)(x3):

=> f(x) = (x + 5) (x - sqrt(3))f(x)=(x+5)(x3)

=> f(x) = (x) (x) + (x) (- sqrt(3)) + (5) (x) + (5) (- sqrt(3))f(x)=(x)(x)+(x)(3)+(5)(x)+(5)(3)

=> f(x) = x^(2) - sqrt(3) x + 5 x - 5 sqrt(3)f(x)=x23x+5x53

=> f(x) = x^(2) - (sqrt(3) - 5) x - 5 sqrt(3)f(x)=x2(35)x53