What is the missing value in the equation 4 2/5

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))

belka [17]

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 $(x-3-\sqrt5)$

8 0

4 years ago

Need help here plss

umka2103 [35]

Answer:

Solutions: b, c, d, e

Not Solutions: a

Step-by-step explanation:

There are two ways to solve this problem: you could graph the system and check which points fall in the solution set or you could substitute the $x$ and $y$ values of each point into the inequalities that make up the system. I'm going to use the former because it's quicker, in my opinion.

Step 1: Graph

Rewriting the first inequality gives us:

$2x+5y$

$5y$

$y$

To graph this, draw the line $y=-\frac{2}{5}x +2$ and then, because the sign is " ", shade below the line and make it a dashed line. This is the red inequality on the graph.

Rewriting the second inequality gives us:

$3x-4y\geq -8$

$-4y\geq -3x-8$

$y\leq \frac{3}{4}x+2$

To graph this, draw the line $y\leq \frac{3}{4}x+2$ and then, because the sign is " $\leq$ ", shade below the line and keep it a solid line. This is the blue inequality on the graph.

The solution set of the system will be the region where the two shaded areas overlap, which is the purple area.

Step 2: Check Points

Now, all we need to do is check whether each point lies in the purple region on the graph.

$(3,5)$ lies above the purple region, but it isn't in the region, so it is not a solution to the system.

$(-2,10)$ does lie in the purple region, so it is a solution to the system.

$(5,-12)$ does lie in the purple region, so it is a solution to the system.

$(-6,-8)$ does lie in the purple region, so it is a solution to the system.

Finally, $(0,0)$ lies in the purple region, so it is a solution to the system.

Hope this helps!

5 0

3 years ago

What is 2x+3x+8-3x-2=

joja [24]

The answer to your question would be 2x + 6!

answer: 2x + 6

(please give thanks)

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3 years ago

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LuckyWell [14K]

We are asked to find f(x) and g(x) so the function can be expressed as y = f(g(x) such that y = y =2/x^(2) + 3. There are many possibilities here but we go to the simplest ones. we can have g (x) = x2 and f(x) is equal to 2/x + 3.

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3 years ago

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Brainliest). The roof of a castle tower is shaped like a cone. The base of the cone is 24 m across and the height is 16 m. The s

larisa [96]

Answer:

base of the cone is 24 m across and the height is 16 m.

Step-by-step explanation:

8 0

3 years ago

What is the missing value in the equation 4 2/5 - 3/n = 4 17/24