Given that x2 +2x -3 is a factors of f (x) = x4 + 6x3 +2 ax2 + b x – 3 a . Find the value of a and b.
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Answer:
a=5,b=(-2)
Explanation:
x²+2x-3=0
x²+3x-1x-3=0
x(x+3)-1(x+3)=0
(x-1)(x+3)=0
x=1,(-3)
→f(1)=(1)⁴+6(1)³+2a(1)²+b(1)-3a=0
f(1)=1+6+2a+b-3a=0
7+b-a=0
a-b=7--------(1)
→ f(-3)=(-3)⁴+6(-3)³+2a(-3)²+(-3)b-3a=0
81-162+18a-3a-3b=0
15a-3b=81
3(5a-b)=81
5a-b=27------------(2)
Subtracting eqⁿ.(2) and eqⁿ.(1):-
5a-a+b-b=27-7
4a=20
a=5
a-b=7
5-b=7
b=(-2)
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