Question

If alpha and beta are then zeros of the polynomial () = x 2 − px + 1 − c then ( + 1) ( + 1)=
a) c-1
b) 1-c
c) c
d) 2`

Answer 1

Answer:

your ans is (b)1-c

Step-by-step explanation:

Given that alpha and beta are roots of quadratic equation

f(x)=x2−p(x+1)−c=x2−px−p−c=x2−px−(p+c)

Comparing with ax2+bx+c,

we have, a=1, b=−p and c=−(p+c)

∴α+β=−b/a=1−(−p)=p and α×β=ac=1−(p+c)=−(p+c)

=(α+1)×(β+1)=(α×β)+α+β+1=−(p+c)+p+1

=−p−c+p+1

=1−c

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