how many zeroes

Question

Without actually solving, I have to explain how many zeroes the function has. I have solved on a seperate paper and I know it has one zero, I just have to explain/know why it has one zero/x-intercept.

This is the function

f(x)=x²-8x+16

Answer 1

check the discriminant

b^2 -4ac where a =1, b=-8 and +16

b^2-4ac = 64-4(16) = 64 -64 = 0

when the discriminant = 0 there is only 1 solution (albeit with multiplicity 2)

if the discriminant were >0 there would be 2 real solutions

if the discriminant were <0 there would be 2 imaginary solutions

if the discriminant = 0, there is only one real solution (but considered to have multiplicity 2, i.e. it repeats twice, when you solve it you get x = 4+ or - 0, or x=4+0 or x=4-0, which gives x= 4, 4)