Question

find a cubic polynomial of degree 3 with real coefficients satisfying the condition f(2)=10 and whose roots include i and 3.

Answer 1

*correction f(2)= -10,,,,need urgent help please

Answer 2

If one of the roots is i, then -i is also a root.
Thus, our cubic equation is:
\[Q(x)=a(x-i)(x+i)(x-3)\\
Q(x)=a(x^2+1)(x-3)\]
Now, plug in x=2 and Q(x)=-10 to find a:
\[-10=a(2^2+1)(2-3)=a(5)(-1)\\
-10=-5a \Rightarrow a=2\]
Then the cubic polynomial is:
\[Q(x)=2(x^2+1)(x-3)=2(x^3-3x^2+x-3)=2x^3-6x^2+2x-6\]

Answer 3

thnx man

Answer 4

No problem. :D