Question

If x2-1 is factor of ax3+bx2+cx+d=0 show a+c=o

Answer 1

Solution is attached below

Answer 2

Step-by-step explanation:

Let f(x)=ax³+bx²+cx+d

As (x²-1) is a factor of f(x).

we have x²-1 = (x+1)(x-1)

Hence , f(1) = 0 and f(1)=0

=> f(1)=a(1)³+b(1)²+c×1+d=0

=> a+b+c+d = 0

=> a+c+b+d=0----(1)

and

f(-1)=a(-1)³+b(-1)²+c(-1)+d=0

=> -a+b-c+d = 0

=> b+d = a+c ---(2)

Substitute this value in equation (1) , we get

a+c+a+c=0

=> 2a+2c=0

=> 2(a+c)=0

=> a+c = 0

and b+d = 0

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