Question

Write a quadratic equation in standard form with 1 over 2
and 3 as its roots

Answer 1

f(x) = 2x² - 7x + 3

Explanation:

Given the roots are x =
`(1)/(2)` and x = 3, then the corresponding factors are

(x -
`(1)/(2)` ) and (x - 3), that is

(2x - 1) and (x - 3)

The equation is then the product of the roots, that is

f(x) = (2x - 1)(x - 3) ← expand factors using FOIL

f(x) = 2x² - 7x + 3 ← in standard form