Find the value of a if (x+a) is a factor of the polynomials x^3+ax^2-2x+a+4
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Here, f(x)= x^3 + ax^2- 2x + a + 4
And, g(x)= x + a
We have, x + a = 0
=> x = -a
Now, put the value thus found into f(x) function
f(-a) = (-a)^3 + a(-a)^2 - 2(-a) + a + 4 =0
=> -a^3 + a^3 + 2a + a = -4
=> 3a = -4
=> a = -4/3
And, g(x)= x + a
We have, x + a = 0
=> x = -a
Now, put the value thus found into f(x) function
f(-a) = (-a)^3 + a(-a)^2 - 2(-a) + a + 4 =0
=> -a^3 + a^3 + 2a + a = -4
=> 3a = -4
=> a = -4/3
uttu12345:
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