If alpha and betaare the zeroes of thequadratic polynomial f(x) = x^2

1.	If alpha and betaare the zeroes of thequadratic polynomial f(x) = x^2 -p ( x+ 1) -c , show that(α+ 1) (β + 1 ) = 1 - c
Answer» To ProvE : (α+ 1) (β + 1 ) = 1 - c SolutioN : <P> $\tt \dagger \: \: \: \: \: Sum \: of \: Zeros.$ $\tt \dagger \: \: \: \: \: \alpha + \beta = \dfrac{ - b}{a}$ $\tt \dagger \: \: \: \: \: product \: of \: Zeros.$ $\tt \dagger \: \: \: \: \: \alpha \beta = \dfrac{c}{a}$ A/Q, We have EQUATION, $\tt \dagger \: \: \: \: \: {x}^{2} - p(x + 1) - c.$ $\tt : \implies {x}^{2} - p(x + 1) - c.$ $\tt \dagger \: \: \: \: \: {x}^{2} - px - p - c.$ Compare with GENERAL Expression. $\tt \dagger \: \: \: \: \: a {x}^{2} + bx + c$ Where as, a = 1. b = -p c = - p - c. Now, → (α+ 1) (β + 1 ) → αβ + α + β + 1. Product of Zeros ( αβ ) → - p - c Sum of Zeros ( α + β ) → p. ★ Putting the GIVEN value on it. → αβ + α + β + 1. → - p - c + p + 1. → - c + 1. Hence Proved.