Question

if alpha ,,beta are the roots of the quadratic equation x2-b(x+1)=0,then (alpha+1)(beta+1)=?

Answer 1

Answer:

correct answer is 1

Step-by-step explanation:

x2-b(x+1)=0

x2-bx-b=0

sum of roots =-b/a=-(-b)/1=b=alpha+beta---(i)

product of roots=c/a=-b/1=-b=alpha.beta---(ii)

(alpha+1)(beta+1)

alpha.beta+alpha+beta+1

-b+b+1-------(from i and ii)

1

therefore 1 is the correct answer

Answer 2

Answer:

alpha is written as c and beta is written as d.

Here, x² - bx - b = 0

Sum of roots = - ve of coefficient of x = c + d = b

Product of roots = constant term = cd = - b.

In question :

→ ( 1 + a )( 1 + b )

→ 1 + b + a + ab

→ 1 + ( sum of roots ) + ( product of roots )

→ 1 + b + ( - b )

→ 1 + b - b

→ 1

Required value is 1