Answer:
2: 3, 4: 6, 6: 9, 8: 12 , 10: 15, 12: 18, 14: 21, 16: 24, 18: 27, 20: 30, 22: 33, 24:36, 26: 39, 28: 42, 30: 45, 32: 48, 34: 51, 36: 54, 38: 57
Step-by-step explanation:
The ratio 4: 6 can be simplified to 2:3 by dividing by 2 to each side of the ratio. After simplified to 2:3, you add the ration to itself to get the rest of the terms.
We can write this as:-
P(x) = + x^3 - 5x^2 - 25x + 125
There are 2 changes of real sign so by Descartes Rule of signs there are either 2 positive real roots or 0 positive roots.
P(-x) = - x^3 - 5x^2 + 25x + 125
There is just one change of sign so there is exactly 1 real negative root.
125 is a multiple of 5 so By rational root theorem 5 could be a positive root.
P(5) = 125 - 125 - 125 + 125 = 0 so one zero is 5
if we divide the polynomial by (x - 5) we get the quadratic
x^2 - 25
(x + 5)(x - 5) = 0
x = 5,-5
so the roots are 5 (multiplicity 2) and -5.
2 real positive zeroes and one real negative zero
