Question

If alpha and beta are the zeros of the polynomial f (x) = x^2 - P(X+1) - C , show that (alpha + 1) (Beta + 1) = 1 - C ​

Answer 1

Answer:

here , f (x)=x^2-px-(p+x)

i.e., x^2+(alpha+beta)x+alpha×beta = x^2-px-(p+c)

comparing both sides,we get:

alpha+beta=p (i)

& alpha×beta=-(p+c) (ii)

L.H.S= (alpha+1)(beta+1)=(alpha×beta)+(alpha+beta)+1=

(p)+{-(p+c)}+1=p-p-c+1=1-c=R.H.S.

verified. .....

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