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## Homework Statement

I'm given two subspaces L and K of P2 (R) are given by

L = { f(x) : 19f(0)+f ' (0) = 0 }

K = { f(x) : f(1) = 0 }.

Obtain a non-trivial quadratic n = ax2 + b x +c such that n is element of the intersetion of L and K.

## Homework Equations

## The Attempt at a Solution

19f(0) =19[a(0)^2+b(0)+c] = 19c

df/dx = 2ax+b...so f'(0) = b. therefore L= {19c+b = 0}.

K = {a+b+c = 0}

let X be an element of both L and K and equate the two equations: So r(19c+b) = s(a+b+c), for r, s reak numbers. 19cr+br =as+bs+cs. c(19r-s)-bs+a(r-s) = 0. I'm stuk from there.. Any help would be appreciated.

Thank you.

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