Question

find the value of a if (x+a) is a factor of x^3+ax^2-2x+a+4

Answer 1

given, p(x)=x^3 + ax^2 - 2x + a + 4 _eq(1)

let g(x ) = x + a = 0 , x = - a

put value of ' x ' in eq(1). we get ,

p(-a)= (-a)^3 + a(-a)^2 - 2(-a) + a + 4

p(-a)= - a^3 + a^3 + 2a + a + 4

p(-a)= 3a + 4

g(x) will be a factor of p(x) if p(-a)=0, so now

p( -a) = 0

3a + 4 = 0

3a = - 4

a = - 4/ 3
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Your Answer: a = - 4/3
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