Question

. If a and ß are the zeros of the quadràtic polynomial f(x) = x² - p(x + 1) - C, show that
(a + 1) (B + 1) = 1 - C​

Answer 1

Answer:

Given: α and β are the zeros of the quadratic polynomial f(x) = x2 - p(x + 1) - c To show: (α + 1)(β + 1) = 1 - c ..... (1) solution: one root of the given quadratic polynomial is α Other root of the given quadratic polynomial is β f(x) = x2 - p(x+1) - cf(x) = x2 - px - p - cf(x) = x2 - px - (p + c) Sum of the roots is: Product of coefficient is: Solve LHS of (1) to get, On substituting values, we get Hence proved