Question

if alpha bita are zeros of polynomial-x²-p(x+1)-q then (alpha+1) ( bita +1) is equal to
(a) q-1
(b) 1-q
(c) q
(d)1+q
please explain step by step​

Answer 1

Correct question : If α and β are the zeros of the polynomial x² - p ( x + 1 ) + c such that, ( α + 1 ) ( β + 1 ) = 0 then find the value of c.

Answer:

c = - 1

Step-by-step explanation:

x² - p ( x + 1 ) + c

⇒ x² - p x - p + c

⇒ x² - p x + ( c - p )

Comparing with ax² + bx + c, we get :

a = 1

b = - p

c = c - p .

Given  :

( α + 1 )( β + 1 ) = 0

⇒ αβ + α + β + 1 = 0

Note that, sum of roots = - b/a

α + β = - b / a

But b = - p

a = 1

So α + β = - ( - p ) / 1 = p

Product of roots = αβ = c / a

⇒ αβ = ( c - p )

Hence write this as :

αβ + α + β + 1 = 0

⇒ c - p + p + 1 = 0

⇒ c + 1 = 0

⇒ c = -1

Hence, the value of c is - 1.