Question

If alpha and beta are the zeroes of of quadratic polynomial x square - p(x+1)-c.show that (alpha+1)(beta+1)=1-c

Answer 1

so question is like this
x²-p(x+1)-c
x²-xp-p-c
x²-xp-(p+c)
alpha is ã and beta is ß
so A.T.Q
(ã+1)(ß+1)=1-c
ãß+ã+ß+1=1-c
ãß+(ã+ß)+1=1-c
we know that
$\alpha \times \beta = \frac{ - (p + c) }{1}$
$\alpha + \beta = \frac{ - ( - p)}{1} = p$
so from above relation
-p-c+p+1=1-c
-c+1=1-c
1-c=1-c
L.H.S=R.H.S
So Hence proved
I hope it works and would be brainiest.