SOLUTION: Hii my beloved tutors, I really need help on this question, could you please help me? Suppose {{{ a }}} is a real number, so that polynomial {{{ p(x)= x^4+4x+a }}} is divisible by

Question 1020769: Hii my beloved tutors, I really need help on this question, could you please help me?
Suppose is a real number, so that polynomial is divisible by for is a real number. What is the value of that satisfies?
Thanks
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
If is to divide , then x-c should be able to divide the latter twice.
Using the remainder theorem, if c is to be root of p(x), then p(c) = 0, or
Now divide by x-c, and letting the remainder equal to 0, we get the polynomial .
By applying the remainder theorem again on this resulting polynomial, we get
The last equation gives .
substitution of this value into gives .
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