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 \(\large k\).

Inspirations - 1 and 2
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