Question

Need answer for this ​

Answer 1

let roots be a and a^2

then

product of roots = c/a = 1 (given)

also product of roots = a^3

=> a = 1, w, w^2 (by equating above two)

a is cube roots of unity

sum of roots = -b/a = -p/3

Also sum of roots = a + a^2

= w + w^2 = -1 (if we choose a = w and use 1+w+w^2=0)

Equating above two

-p/3 = -1

=> p = 3.

If we choose a = 1

we get p = -2/3 (not possible as p>0)

if we choose a = w^2

then sum of roots = w^2+w^4

= w(w + w^3)

=w(w + 1)

=w^2 + w = -1

=> -p/3 = -1

=> p = 3. Answer