Question

hey

plz ans my question
first ans will be marked ​

Answer 1

$\textbf{Answer is in Attachment !}$

Answer 2

Answer:

Given function :

f(x) = x² - p (x + 1) - c

⇒ f(x) = x² - p x - p - c

Comparing with a x² + b x + c we get :

a = 1

b = -p

c = - p - c

Sum of roots = - ( coeffecient of the second term ) / ( coefficient of the first term )

α + β = -b/a

α + β = -(-p)/(1)

α + β = p

Product of roots = ( coeffecient of the last term ) / ( coefficient of the first term ) for even degree equations .

αβ = c/a

αβ = ( - p - c )/1

αβ = - p - c

( α + 1 )( β + 1 )

αβ + α + β + 1

⇒ p - c - p + 1

⇒ 1 - c

The answer is OPTION (2)

Step-by-step explanation:

The general form of a quadratic equation is given by :

a x² + b x + c = 0 where a ≠ 0 and the highest power of the equation should be 2 .

The given equation has roots α and β . We need to use the sum of roots and product of roots and use an algebraic identity .

The algebraic identity used is :

( x + a )( x + b ) = x² + x ( a + b ) + a b