If 1 and -1 are zeroes of the polynomial Lx rays to 4 +Mx³+Nx²+Rx+P, then show that L+N+P=M+R
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The given polynomial is p(x) = Lx4+Mx3+Nx2+Rx+P
Since 1 and (-1) are the zeroes of the polynomial so we have;
p(1) = L×(1)4+M×(1)3+N×(1)2+R×1+P = 0⇒L+M+N+R+P = 0 ...(1)p(−1) = L×(−1)4+M×(−1)3+N×(−1)2+R×(−1)+P = 0⇒L−M+N−R+P = 0 ....(2)
Now from (1) and (2) equation, we get
2M+2R=0
M+R=0........(3)
now from (1) and (3) we get
L+N+P=0......(4)
so from 3 and 4 equation we get
L+N+P =M+R
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Since 1 and (-1) are the zeroes of the polynomial so we have;
p(1) = L×(1)4+M×(1)3+N×(1)2+R×1+P = 0⇒L+M+N+R+P = 0 ...(1)p(−1) = L×(−1)4+M×(−1)3+N×(−1)2+R×(−1)+P = 0⇒L−M+N−R+P = 0 ....(2)
Now from (1) and (2) equation, we get
2M+2R=0
M+R=0........(3)
now from (1) and (3) we get
L+N+P=0......(4)
so from 3 and 4 equation we get
L+N+P =M+R
if my answer is helpful for you then please mark as brain liest
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Answered by
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Answer:
Step-by-step explanation:
1 is zero of polynomial.
substitute 1 in place of x and equate to zero
L(1)^4+M(1)^3+N(1)^2+R(1)+P=0
L+M+N+R+P=0----------(1)
-1 Is zero of polynomial
sub -1 in place of x
L-M+N-R+P=0
L+N+P=M+R----(2)
From 1&2 we get L+N+P=M+R=0
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