Question

If a and b are the roots of the quadratic equation x2- p ( x+1 ) - c = 0,then find the value of ( a + 1 ) ( b + 1 ).

Answer 1

Answer:

1 - c

Step-by-step explanation:

We know,

         quadratic polynomial in the form x^2 - Sx + P represents the sum and product of its roots as - S and P.

So, here, polynomial is x^2 - p( x + 1 ) - c = 0   ⇒ x^2 - px - p - c = 0     ⇒ x^2 - px - ( p + c ) = 0

      Sum of roots = - S = - p

                            = S = p

       Product of roots = - ( p + c  )

⇒ ( a + 1 )( b + 1 )

⇒  ab + a + b + 1

⇒ sum of roots + product of roots + 1

⇒ p - ( p + c ) + 1

⇒ p - p - c + 1

⇒ 1 - c

Answer 2

AnswEr :

Value of (1 + a)(1 + b) is 1 - c

Explanation :

Given Polynomial,

p(x) = x² - p(x + 1) - c

» p(x) = x² - px -(p + c)

If a and b are the zeros of the above polynomial,

• a + b = - (-p) = p

• ab = - (p + c)

$\rule{300}{1}$

Now,

(a + 1)(b + 1)

= 1² + (a + b) + ab

= 1 + p - (p + c)

= 1 - c

$\rule{300}{1}$

$\rule{300}{1}$