Question

If one zero of the polynomial x^2-4x+1 is 2+root 3,write the other zero

Answer 1

Usually if one root is irrational, the other would be the conjugate of it. So, the other root should be 2-root3. If you want to verify, the product should be equal to 1 (c/a) and sum should be equal to -(-4)=4 (b/a). This holds true, so the other root is 2-root3.

Answer 2

p(x)= x^2-4x+1

This can be written in the form ax^2+bx+c where, a= 1, b=-4, c=1

One zero is 2+ root 3

i.e; alpha=2+ root 3

Beta=?

Sum= alpha + beta = -b/a

(2+root3) + beta =-(-4)/1

Beta= 4-(2+root3)

=4-2-root3

=2-root3

Hence, the other zero is 2- root3