Question

Write an equation of the quadratic function that has x-intercepts 5-i√2 and 5+i√2

Answer 1

Answer:

f(x) = x² - 10x + 27

Step-by-step explanation:

Given the x- intercepts of f(x) are x = a and x = b, then the factors are

(x - a) and (x - b) and f(x) is the product of the factors, that is

f(x) = (x - a)(x - b)

Here the x- intercepts are 5 - i$\sqrt{2}$ and 5 + i$\sqrt{2}$ , thus the factors are

(x - (5 - i$\sqrt{2}$ )) and (x - (5 + i$\sqrt{2}$ )) , that is

(x - 5 + i$\sqrt{2}$) and (x - 5 - i$\sqrt{2}$ , then

f(x) = (x - 5 + i$\sqrt{2}$ )(x - 5 - i$\sqrt{2}$ ) ← expand using FOIL

     = (x - 5)² - 2i² ← i² = - 1

     = x² - 10x + 25 + 2

     = x² - 10x + 27