If (x - 2) is the real factor of many terms f (x) = x^3 - bx^2 + 2x + 8, then the quotient
f (x) where (x - 2) is ...
a. x^2 - 3x - 4
b. x^2 + 3x - 4
c. x^2 + 3x + 4
d. x^2 - 4x - 3
e. x2 + 4x - 3
Answers
Answer:
How do I find the value of a and b with the polynomial f(x)=2x3+ax2−bx+3" ??
What are the most available online courses to learn algorithmic trading and quantitative finance?
Nowadays, there are a plethora of courses available teaching different aspects of algorithmic trading. But if you are serious a...
Let us see the polynomial f(x) = 2x^3 +ax^2 - bx + 3.
(x+3) is one factor which means x = -3. Substitute -3 for x to get
-54 +9a + 3b + 3 =0, or dividing by the HCF, which is 3 we get
-18 + 3a + b +1 = 0, or
3a + b = 17 … (1).
When divided by (x-2) the polynomial yields a remainder of 15. So deduct 15 from the polynomial to get 2x^3 +ax^2 - bx + 3 - 15, or
2x^3 +ax^2 - bx -12. This polynomial should be divisible by (x-2) without leaving a remainder. Hence x=2. Substitute 2 for x in
2x^3 +ax^2 - bx -12, to get
16 + 4a - 2b - 12 = 0, or
4a - 2b = -4, or
2a - b = -2 … (2).
Add (1) and (2) to get
5a = 15 o...