Question

if alpha beta are the zeros of the polynomial f of x x square - p into X + 1 - C such that alpha + 1 and 2 Beta + 1 such that alpha plus 1 into beta plus 1 = 0then c is equal to ?​

Answer 1

f(x)= x²-p(x+1)-c

=x²-px-p-c

since , alpha and beta are zeroes

therefore, sum of zeroes =-b/a

alpha + beta = -(-p)/1

alpha +beta = p

also,

product of zeroes = c/a

alpha.beta = -p+c

now,

(alpha+1)(beta+1)=0

alpha.beta +alpha + beta+1= 0

substituting the above values:-

-p+c+p+1=0

c+1=0

c=-1

values of c is -1