Question

If one zero of the quadratic polynomial ax^2 + bx + c is cube of the other, then the value of the sum of the cubes of both the zeroes is
(1) b^3 + abc / 3a^3
(2) a^3 + b^3 / 3abc
(3) a^3 - 3abc / b^3
(4) 3abc - b^3 / a^3​

Answer 1

Answer:

solved

Step-by-step explanation:

ax² + bx + c = 0

roots = ∝ , β

β = ∝³

then roots are ∝ , ∝³

∝³ + ∝  = -b/a

∝∧4 = c/a

it is required to find ∝³ +  β³

∝³ +  β³ =  ∝∧9 + ∝³ = (∝³)³ + ∝³ =  (  ∝³ + ∝) (  ∝∧6 -  ∝ ∧4+ ∝²)

= ∝² (  ∝³ + ∝) (  ∝∧4 -  ∝² + 1 )