Question

find the condition that x²-px²+ qx-r = 0 may have sum of two of its roots is zero​

Answer 1

Step-by-step explanation:

Given,

x

3

−px

2

+qx−r=0

say the cubic equation has roots a,−a,b

then

a+−a+b=(−1)(−p)⟶(1)

a(−a)+a(b)+(−a)b=+q⟶(2)

a(−a)b=(−1)(−r)⟶(3)

∴ From (1) we have,

b=p⟶(4)

From (2) we have

−a

2

=q⟶(5)

From (3) we have

−a

2

b=r⟶(6)

Using (4) & (5) we can write (6) as

+qp=r (∵ −a

2

=q,b=p)

⇒r=pq