x² - 2xm - 2kx + 4km
Step-by-step explanation:
Roots of the equation: 2k and 2m
This means x = 2k or x = 2m
x - 2k = 0 or x - 2m = 0
we bring the factors together:
(x - 2k)(x - 2m) = 0
Expand:
x(x - 2m) -2k(x - 2m)
x² - 2xm -2kx + 4km
we can't add the coefficent of x together because the constant k and m are not known.
Hence, the quadratic equation whose roots are 2k and 2m is x² - 2xm - 2kx + 4km