Question

please solve these questions
14th question

Answer 1

Hey Sheil ,

Here is your solution :

Given,

Quadratic equation = x² - p( x + 1 ) - c = x² - px - p - c.

α and ß are its zeroes.

Here,

Coefficient of x² ( a ) = 1

Coefficient of x ( b ) = -p

Constant term ( c ) = - ( p + c ).

Now,

⇒ Sum of zeroes = -b/a

⇒ α + ß = - ( -p ) ÷ 1

⇒ α + ß = p   ----------- ( 1 )

And ,

⇒ Product of zeroes = c/a

⇒ αß = - ( p + c ) ÷ 1

∴ αß = - ( p + c ).

Now,

⇒ ( α + 1 ) ( ß + 1 ) = 1 - c

⇒ αß + α + ß + 1 = 1 - c

⇒ ( αß ) + ( αß ) + 1 = 1 - c

By substituting the values of ( α + ß ) and αß.

⇒ - ( p + c ) + p + 1 = 1 - c

⇒ -p -c + p + 1 = 1 - c

⇒ -p + p + 1 - c = 1 - c

∴ 1 - c = 1- c.


Proved !!

Hope it helps !!