Question

If the polynomial X cube + 2xsquare+ax+b has factor x+ 1 and x-1, find the value of a and b

Answer 1

x³+2x²+ax+b has factors x+1,x-1
so by substituting x = -1,+1 we can get the answer
so x=-1
x³+2x²+ax+b=0
(-1)³+2(-1)²+a(-1)+b=0
-1+2-a+b=0
=>a-b=1. ------ eq 1
so x=+1
1³+2(1)²+a(1)+b=0
1+2+a+b=0
=>a+b=-3. ------ eq 2
so by adding eq 1,2
=>2a=-2
=>a=-1
so by substituting a=-1 in eq 1or 2
we get b=-2
so (a,b)=(-1,-2)
hope this answer helps you
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