Question

if alpha,beta are the zeroes of p(x)= x²- k(x+1) - c ,then alpha ,beta +(alpha+beta)+1=​

Answer 1

Step-by-step explanation:

x²-k(x+1)-c=0

x²-kx-k-c=0

alpha +beta =k

alpha x beta =-k-c

Answer 2

Step-by-step explanation:

The given quadratic equation is,

p(x)= x²- k(x+1) - c

-> p(x)= x²-kx-c-1.

Now on comparing this with the general form of quadratic equation we have p(x)= ax²+bx+c.

We get on comparing a=1,b=-k and c=-(k+c).

Now we know that sum of the roots=alpha+beta= -b/a=-(-k)/1=k

also,product of the roots =alpha.beta=c/a= -k-c.

Now according to the required condition

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

-k-c+k+1=0

1-c=0

HENCE THE VALUE OF THE ABOVE CONDITION IS 1-C=0