Question

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Answer 1

$\mathfrak{ \huge \underline{Given:}}$

Zeroes of polynomials $Lx^4+Mx^3+Nx^2+Rx+P$are 1 and - 1

$\mathfrak{ \huge \underline{Answer:}}$

Putting the value of x = - 1 in $Lx^4+Mx^3+Nx^2+Rx+P$, we get

$L-M+N-R+P= 0$

So,it will evaluate to L+N+P= - (-M-R) = M+R

Answer 2

Step-by-step explanation:

Given:-

If 1 and -1 are zeroes of Lx⁴+Mx³+Nx²+Rx+P .

To show:-

L+N+P=M+R=0

Solution:-

Given polynomial is p(x)=Lx⁴+Mx³+Nx²+Rx+P

If 1 is a zero then it satisfies the given polynomial

p(1)=0 by Factor theorem

=>p(1)=L(1)⁴+M(1)³+N(1)²+R(1)+P=0

=>L+M+N+R+P=0---(1)

If -1 is a zero then it satisfies the given polynomial

is a zero then it satisfies the given polynomialp(-1)=0 by Factor theorem

=>p(-1)=L(-1)⁴+M(-1)³+N(-1)²+R(-1)+P=0

=>L-M+N-R+P=0

=>L+N+P=M+R------)(2)

From (1)&(2)

L+N+P=M+R=0

Answer:-

L+N+P=M+R=0