Polynomial function equation

Question

write an equation of a polynomial function of least degree with rational coefficients and the roots 5 and I

Answer 1

write an equation of a polynomial function of least degree with rational coefficients and the roots 5 and I

If the roots of the function are 5 and 1 this means that x = 5 and x = 1.

Begin by setting both roots equal to zero

x - 5 = 0 and x - 1 = 0

Now multiply the two factors:

(x - 5)(x - 1)

x² - x - 5x + 5

Combine like terms:

x² -6x + 5