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alexgriva [62]
4 years ago
7

Please I need help It’s timed!!

Mathematics
1 answer:
alukav5142 [94]4 years ago
3 0

Answer:

I think it's a c and d sorry if I'm wrong

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If a polynomial function f(x) has roots 3+root5 and -6, what must be a factor of f(x)? (X+(3-root5) (x-(3-root5)) (x+(5+root3))
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Answer:

(x-(3+\sqrt5)) or (x-3-\sqrt5) is a factor of the given polynomial.

Step-by-step explanation:

Let us learn the concept with an example first.

Let the polynomial be a quadratic function g(x).

g(x) = x^{2} -5x+6

The roots of g(x) are 2 and 3.

Putting x= 2\ in \ g(x)

2^2-5\times 2+6 = 4-10+6 =0

Putting x= 3\ in \ g(x)

3^2-5\times 3+6 = 9-15+6 =0

Putting x = 2 or x = 3, g(x) = 0 \therefore The roots of equation g(x) are 2 and 3.

Now, let us try to factorize g(x):

x^{2} -2x-3x+6\\\Rightarrow x(x -2)-3(x-2)\\\Rightarrow (x-3)(x-2)

so, the equation can be written as:

g(x) = x^{2} -5x+6=(x-3)(x-2) where 3 and 2 are the roots of equation.

The factors are (x-3) and (x-2).

\therefore for the polynomial f(x) which has roots 3+\sqrt5\ and\ -6 will have a factor:

(x-(3+\sqrt5)) or (x-3-\sqrt5)

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Step-by-step explanation:

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Step-by-step explanation:

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