If 1 and –1 are zeroes of polynomial Lx4 + Mx3 + Nx2 + Rx + P, show that L + N + P = M + R = 0.

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Rajesh Devendrasingh Gusain

Let f(x) = given polynomial f(1)= L+m+n+r +p=0 f(-1)=L-m+n-r+p =0 Subtracting both we get 2m+2r+2p=0 ie m+r+p=0 Adding we get L+r+p=0 ie m+r+p = L+r+p
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Given, F(1)=0 =>L+M+N+R+P=0.....eqn1 Also F(-1)=0 =>L+N+P=M+R.....eqn2 Compare eqn 1and 2 we obtain L+N+P=M+R=0
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