jnu maths doubt

[SoniaKapoor]

pls help.

[Noel]

Should be a
use the fact that if ax^2+bx+c=0 has roots p and q then
p+q= (-b/a)
p.q=c/a

[Anjali]

Option A

[SoniaKapoor]

noel,anjali...i'm not getting it:(..pls explain

[Ankur9]

For an equation ax^2 + bx + c

sum of roots = -(b/a)
product of roots = (c/a)

For the given equation x^2-bx+c

sum of roots = p+q = b
product of roots = pq = c

Roots of the required equation are:
pq+p+q = c+b
pq-p-q = c-b

Equation would be the product:   (x-(c+b))(x-(c-b))

[Noel]

x^2-bx+c=0 has roots p and q
so sum of roots = -(-b)/1 = b
and product of roots = c/1 =c
i.e. p+q=b and p.q=c  (1)
now let the equation Ax^2+Bx+C=0 have the roots (pq+p+q) and (pq-p-q)
(pq+p+q)+(pq-p-q)= -B/A
2pq= -B/A
from equation (1)
2c= -B/A
and (pq+p+q).(pq-p-q) = C/A
again from equation (1)
(c+b).(c-b)=C/A
c^2-b^2=C/A
it is clear that A=1
B = (-2c)
C= c^2-b^2
hence the equation is
x^2-2cx+(c^2-b^2)=0
hope this helps :)