P(x)=x⁶-x⁵-x³-x²-x Q(x)=x⁴-x³-x²-1. If α, β, γ and δ be the roots of Q(x)=0, then find P(α)+P(β)+P(γ)+P(δ)

Algebra question

Medium · from the problemset algebra collection

$$P(x)=x^6-x^5-x^3-x^2-x \quad Q(x)=x^4-x^3-x^2-1. \text{ If } \alpha,\beta,\gamma\text{ and }\delta \text{ be the roots of } \\ Q(x)=0, \text{ then find } P(\alpha)+P(\beta)+P(\gamma)+P(\delta)$$

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