Question

if alpha, beta are zeros of p(x) =x3-k(x+1)c then alpha*beta+(alpha+beta) =......

Answer 1

Answer:

alpha +beta +(alpha*beta) =0

Step-by-step explanation:

p(x)=x2 - k(x+1)c

     = x2 - kcx -kc

Now, comparing p(x) with the standard form of a quadratic equation, i.e, f(x)= ax2 + bx + c.

a = 1    ;    b = -kc   ;     c= -kc.

if alpha and beta are the roots, then:

alpha+beta= -b/a

thus, alpha + beta= -(-kc)/1 = kc -----------> eq 1

Also,

alpha*beta= c/a

thus, alpha*beta=(-kc)/1 =-kc ----------------> eq2

Therefore, substituting the values from eq 1 and 2

alpha +beta +(alpha*beta) = kc + (-kc) = kc -kc = 0