Bit of eqn .

Great question --- though not difficult ---

If the polynomial

xⁿ + p₁ x^n-1 + p₂ x^n-2 + p₃ x^n-3 + ...... + p_n-1 x + p_n = 0 ,

has n real roots a , b ,c , d ... k , and p₁ , p₂ , p₃ are all real ,

then find the value of ,

( 1 - p₂ + p⁴ ....... )² + ( p₁ - p₃ + p₅ - ....... ) ² in terms of a , b , c , d ........ k .

2 Answers

put x=i

you will get

(p_n-p_n-2+p_n-4-p_n-6.......) + i(p_n-1-p_n-3+p_n-5.....) = (i-a)(i-b)....(i-k)

take modulus on both sides and square..

you get that the given expression is (1+a²)(1+b²)......(1+k²)

Sir , you totally killed it :)

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