# Inspired by Yash Singhal

Algebra Level 5

Let $$a$$ and $$b$$ be the roots of the quadratic equation $x^2-(k-2)cx-(k-1)d=0$

Let $$c$$ and $$d$$ be the roots of the quadratic equation $x^2-(k-2)ax-(k-1)b=0$

If $$a,b,c$$ and $$d$$ are distinct, non zero real numbers such that

$\large{a+b+c+d=100}$

Find the integral value of $$\large k$$.

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