Squary Polynomial

Algebra Level 4

Let f(x)f(x) be a monic quartic polynomial such that ,

f(0.5)=2516f(0.5)=\frac{25}{16}

f(0.3)=10081f(0.\overline{3})=\frac{100}{81}

f(0.25)=289256f(0.25)=\frac{289}{256}

f(0.2)=676625f(0.2)=\frac{676}{625}

Evaluate : ϕ(f(10)+f(9))\phi \left (f(10)+f(9) \right )

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