If the polynomial p(x)=x^4+ax^4+2x^2-3x+b is exactly divisible by x^2-1, find the value of a & b.
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Sol:
if x2- 4 is a factor of ax4+ 2x3- 3x2+ bx - 4.
x2 - 4 = 0 ⇒ x = ±2 are zeros of the polynomial p(x) = ax4+ 2x3- 3x2+ bx - 4.
∴ p(2) = 0 and p(-2) = 0.
p(2) = 0 then 16a + 16 -12 +2b -4 = 0
16a + 2b = 0 -------------(1)
p(-2) = 0 then 16a -16 -12 - 2b - 4 = 0
16a -2b = 32 -------------(2)
Substract (2) from (1) we get
4b = -32
b = -8
Substitute b is in equ(1) we get 16a - 16 = 0
∴ a = 1 and b = -8.
if x2- 4 is a factor of ax4+ 2x3- 3x2+ bx - 4.
x2 - 4 = 0 ⇒ x = ±2 are zeros of the polynomial p(x) = ax4+ 2x3- 3x2+ bx - 4.
∴ p(2) = 0 and p(-2) = 0.
p(2) = 0 then 16a + 16 -12 +2b -4 = 0
16a + 2b = 0 -------------(1)
p(-2) = 0 then 16a -16 -12 - 2b - 4 = 0
16a -2b = 32 -------------(2)
Substract (2) from (1) we get
4b = -32
b = -8
Substitute b is in equ(1) we get 16a - 16 = 0
∴ a = 1 and b = -8.
Animesh764:
its not x^2-4 its x^2-1
Answered by
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since 1 and -1 are its zeros so put them in first eq
u will get 2 linear eq. in a and b and u can solve them easily
u will get 2 linear eq. in a and b and u can solve them easily
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what to do after gettin 2 linear equations
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