#f(x) = 3x^2+ax+bx^2-7x-4#: Given that #(x^2-1)# is a factor of #f(x)#, find #a and b# ?

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Answer 1 · 2017-10-18T11:30:49

#a=7, b=1#
#f(x) = 4(x^2-1)#

#f(x) = 3x^2+ax+bx^2-7x-4#

#= (3+b)x^2+(a-7)x-4#

We are told that #(x^2-1)# is a factor of #f(x)#

Hence, #f(x) =0 -> (x^2-1)=0#

#:.x^2 =1 -> x=+-1#

#f(+1) = (3+b) +(a-7) -4 =0# [A]

#f(-1) = (3+b) - (a-7) -4 =0# [B]

[A] + [B]: #6+2b -8 =0#

#2b = 2 -> b=1#

#b=1# in [A]: #4 +a-7-4=0#

#a=7#

Hence, #f(x) = (3+1)x^2 +(7-7)x -4#

#= 4x^2-4 = 4(x^2-1)#