Find the value of a so that x-1 are the factors of x4-a x3-3 x2-2-2

It is given that (x+1) is a factor of x4+ax3 3x2+2+2 then, x= 1 willbe the root of the equation x4+ax3 3x2+2+2 = 0 Putting x=( 1), ( 1)4+a( 1)3 3( 1)2+2+2 = 0 ...

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Standard IX

Mathematics

Factor Theorem

Find the valu...

Question

Find the value of a so that (x+1) are the factors of x⁴+ax³-3x²+2+2

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Solution

It is given that (x+1) is a factor of x⁴+ax³-3x²+2+2 then,
x= -1 willbe the root of the equation x⁴+ax³-3x²+2+2 = 0

Putting x=(-1),
(-1)⁴+a(-1)³-3(-1)²+2+2 = 0

1-a-3+4 = 0

a =1+4-3 =2

So a=2

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Find the values of a and b so that(x-1) and (x+1) are the factors of x⁴+ax³-3x²+2x+b

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Find the value of a so that (x+1) are the factors of x4+ax3-3x2+2+2

It is given that (x+1) is a factor of x4+ax3-3x2+2+2 then, x= -1 willbe the root of the equation x4+ax3-3x2+2+2 = 0 Putting x=(-1), (-1)4+a(-1)3-3(-1)2+2+2 = 0 1-a-3+4 = 0 a =1+4-3 =2 So a=2

Find the value of a so that (x+1) are the factors of x⁴+ax³-3x²+2+2

It is given that (x+1) is a factor of x⁴+ax³-3x²+2+2 then,
x= -1 willbe the root of the equation x⁴+ax³-3x²+2+2 = 0

Putting x=(-1),
(-1)⁴+a(-1)³-3(-1)²+2+2 = 0

1-a-3+4 = 0

a =1+4-3 =2

So a=2