Question

Find relation between p,q,r if the root of the cubic equation x^3-px^2+qx+r=0 are such that they are in ap

Answer 1

Hence, sum of roots of a cubic equation = -(-p) = p 

a+b+y = p

Now, its given that a+b = 0

hence y = p

 

Also, product of roots =-( -r)

Hence aby = r 

 

Also, ab+by+ya = q

 

Now pq = (y) (ab+y(a+b))

pq =  y(ab) (Since a+b = 0)

pq = r

 

Answer 2

Answer:

pq = r

Step-by-step explanation:

Hence, sum of roots of a cubic equation = -(-p) = p

a+b+y = p

Now, its given that a+b = 0

hence y = p

Also, product of roots =-( -r)

Hence aby = r  

Also, ab+by+ya = q

Now pq = (y) (ab + y (a + b))

pq =  y (ab)                   (Since a+b = 0)

pq = r