f(x) = x^2 - 4x +2

Question

Approximate the real zeros

Answer 1

there's potentially 2 zeroes for x^2 -4x +2

It doesn't factor. That leaves completing the square

f(x) = x^2 -4x + 4 = -2 +4

(x-2) = sqr2

x = 2 + or - sqr2 = 3.1414 or 0.8586

for any quadratic, degree 2 polynomial, there's 0, 1 or 2 real zeroes.

for x=0 f(x) = 2

for x=1 f(x) =-1

there must be a zero in between x=0 and x= 1, maybe x = 3/4, a little closer to x=1 than to 0

.75 is close to .86 the actual solution

for x=3 f(x) = 9-12+2 =-1

for x=4 f(x) = 16-16+2 = 2

since f goes from negative to positive when x goes from 3 to 4, the zero must be between 3 and 4, but closer to 3 as -1 is closer to 0 than +2, about a 1/3 closer, maybe 3.3 which is close to the actual zero of 3.14