Question

find the condition such that one root of the equation ax²+bx+c=0 is square of the other.​

Answer 1

Step-by-step explanation:

Let p and p^2are the roots of ax^2+bx+c= 0

p+p^2 = -b/a……………(1)

p.p^2 = c/a

p^3 = c/a………………….(2)

On cubing eq.(1) both sides

p^3 + p^6 +3.p.p^2.(p+p^2) = (-b/a)^3

On putting the values of eq.(1( & (2).

c/a + (c/a)^2 +3.c/a.(-b/a) = -b^3/a^3

c/a + c^2/a^2 - 3b.c/a^2 = -b^3/a^3

On multiplying both sides by a^3

c.a^2 + c^2.a - 3a.b.c = -b^3

or b^3 + c.a(c+a) = 3.a.b.c .