Q. 144.1( 22 Votes )

# If α and β are the zeros of the quadratic polynomial , show that .

Given:α and β are the zeros of the quadratic polynomial

To show: ..... (1)

solution:

one root of the given quadratic polynomial is

Other root of the given quadratic polynomial is β

f(x) = x2 - p(x+1) - c

f(x) =  x2 - px - p - c

f(x) = x2 - px - (p + c)

Sum of the roots is:

Product of coefficient is:

Solve LHS of (1) to get,

+1

On substituting values, we get

= -(p+c) + p + 1

=

⇒  =

Hence proved

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