You have shared the situation (problem), except for the directions: What are you supposed to do here? I can only make a educated guesses. See below:
Note that if <span>ax^2+bx+5=0 then it appears that c = 5 (a rational number).
Note that for simplicity's sake, we need to assume that the "two distinct zeros" are real numbers, not imaginary or complex numbers. If this is the case, then the discriminant, b^2 - 4(a)(c), must be positive. Since c = 5,
b^2 - 4(a)(5) > 0, or b^2 - 20a > 0.
Note that if the quadratic has two distinct zeros, which we'll call "d" and "e," then
(x-d) and (x-e) are factors of ax^2 + bx + 5 = 0, and that because of this fact,
- b plus sqrt( b^2 - 20a )
d = ------------------------------------
2a
and
</span> - b minus sqrt( b^2 - 20a )
e = ------------------------------------
2a
Some (or perhaps all) of these facts may help us find the values of "a" and "b." Before going into that, however, I'm asking you to share the rest of the problem statement. What, specificallyi, were you asked to do here?
Answer:
A. 4
B. 1
Step-by-step explanation:
The degree of a one-variable polynomial is the largest exponent of the variable.
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<h3>A.</h3>
For f(x) = x^4 -3x^2 +2 and g(x) = 2x^4 -6x^2 +2x -1, the sum f(x) +a·g(x) will be ...
(x^4 -3x^2 +2) +a(2x^4 -6x^2 +2x -1)
= (1 +2a)x^4 +(-3-6a)x^2 +2ax -a
The term with the largest exponent is (1 +2a)x^4, which has degree 4. This term will be non-zero for a ≠ -1/2.
The largest possible degree of f+ag is 4.
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<h3>B.</h3>
The polynomial sum is ...
f+bg = (1 +2b)x^4 +(-3-6b)x^2 +2bx -b
When b = -1/2, the first two terms disappear and the sum becomes ...
f+bg = -x +1/2 . . . . . . a polynomial of degree 1
The smallest possible degree of f+bg is 1.
1,2 and 5 is the answers I think
Remember, there is a missing term which is crucial to solving this, and that is 0x.
Ima use synthetic division, because that's the quicker option here:
The zero of x+2 is -2...
-2 | 3 5 1 0 -5
-6 2 -6 12
_____________
3 -1 3 -6 7
(Sorry, I'm unsure how to fix the formatting, plus I'm new to this. The -6 and such on the second line should be below the 5 and following of the first line, and the 3 and such on the last line should be below the 3 and following on the first line, leaving a space between the 3 on the first and third line.)
So the answer is: A. 3x^3 - x^2 + 3x - 6 + 7/(x+2)
