Question

If a and B are the roots of x2 - p(x + 1) - C = 0,
then the value of (a + 3)(B+3) if p = 1, is​

Answer 1

Answer:

c = - 1

x² - p ( x + 1 ) + c

⇒ x² - p x - p + c

⇒ x² - p x + ( c - p )

a = 1

b = - p

c = c - p .

( 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.

Step-by-step explanation: