If [tex]x^2-1[/tex] is a factor of [tex]x^3-ax^2+bx+2[/tex] then find value of a and b
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tex] then find value of a and b
If [tex]x^2-1[/tex] is a factor of [tex]x^3-ax^2+bx+2[/tex] then find value of a and b
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Answer:
a = 2 , b= -1
Step-by-step explanation:
see in the attachment .
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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