Question

If alpha and beta are zeroes of the polynomial x^2 - a(x+1)​

Answer 1

if alpha and beta are zeroes of the poly.x^2-a(x+1)then,p(alpha)=0andp(beta)=0

Answer 2

Answer:

The required numeric value of b is 1.

Step-by-step explanation:

It is given that α and β are the zeroes of the polynomial x^2 - a( x + 1 ) - b. Also ( α + 1 )( β + 1 ) = 0.

First of all, as the α and β are the zeroes, it means that x^2 - a( x + 1 ) - b is equal to 0.

Thus, x^2 - a( x + 1 ) - b = 0

Also, given that ( α + 1 )( β + 1 ) = 0

By Zero Product Rule : α + 1 = 0 Or/And β + 1 = 0

= > α = - 1 Or/And β = - 1

Now, substituting the value of α and β one by one in the given polynomial :

But in both the cases, we will get the same result. So :

Satisfactory Case : Substituting the value of α or β, which is a root of x, it means that one value of x is - 1.

= > x^2 - a( x + 1 ) - b = 0

= > ( - 1 )^2 - a( - 1 + 1 ) - b = 0

= > 1 - a( 0 ) - b = 0

= > 1 - b = 0

= > 1 = b

Hence the required numeric value of b is 1.