# Real roots are demanded!

**Algebra**Level 4

For some real number \(k\) independent of \(x\), the polynomial \(f(x) = 2x^{3}-9x^2+12x-k\) have all real roots.

Given that \(m<k<n\), find the value of \(mn(n-m) \).

For some real number \(k\) independent of \(x\), the polynomial \(f(x) = 2x^{3}-9x^2+12x-k\) have all real roots.

Given that \(m<k<n\), find the value of \(mn(n-m) \).

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