(5 + 61) - (12 + 71)

Answer:

Equation 3

Step-by-step explanation:

Lets see which of the functions has -2 as a zero root. We will go in order:

(1) (-2)^4 - 3(-2)^3 + 3(-2)^2 -3(-2) + 2 = 16 - 3(-8) + 3(4) + 6 +2 = 16 +24 +12 + 6 +2 =60 >0

So, (1) is wrong!

(2) (-2)^4 + 3(-2)^3 + 3(-2)^2 - 3(-2) - 2 = 16 - 24 + 12 + 6 - 2 =34 - 26 = 8 > 0

(2) is also wrong!

(3) (-2)^4 + 3(-2)^3 + 3(-2)^2 +3(-2) + 2 = 16 - 24 + 12 - 6 + 2 = 30 -30 = 0

The zero root x=-2 fits, what about x=-1?

(-1)^4 + 3(-1)^3 + 3(-1)^2 +3(-1) + 2 = 1 - 3 + 3 - 3 + 2 = 6 - 6 = 0

So, equation (3) fits both!

Finally, lets see (4):

(-2)^4 - 3(-2)^3 - 3(-2)^2 + 3(-2) + 2 = 16 + 24 - 12 - 6 + 2 = 42 - 18 = 24 > 0

So, (4) is also wrong.

Only equation 3 fits both zero roots!

Final answer:

The quartic function with x=-1 and x=-2 real roots is x^4+6x^3 +12x^2+12x+4. Quartic functions are polynomial functions of degree 4; quadratic equations resources also help understand the concept. In essence, finding roots of quartic functions follow the same logic as that of quadratic functions.

Explanation:

The subject matter pertains to quartic functions in mathematics. Quartic functions are polynomial functions with a degree of 4. From the question, the given zeros are x=-1 and x=-2, having multiplicity of 2 each (since there are only two real zeros). Thus, the quartic function with these zeros will be (x+1)^2*(x+2)^2. This can be expanded to x^4+6x^3 +12x^2+12x+4.

Exemplifying the relevance of The Solution of Quadratic Equations, normally known as second-order polynomials or quadratic functions, such equations can also be used to find zeros of the functions when set to equal zero. In this scenario, quartic functions are a degree higher, but the same principle applies in finding the roots when the equation is set equal to zero.

Learn more about Quartic Functions here:

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Answer:

20:36

Step-by-step explanation:

5:9

multiply both parts of the ratio by 4

5 x 4 = 20

9 x 4 = 36

So 20:36 is equivalent to 5:9

Answer:

A) 32

Step-by-step explanation:

From 1 to 10 we have 4 numbers which are {2,4,6,8}

From 10 to 20 we have 4 numbers which are {12,14,16,18}

.

.

.

From 70 to 78 we have 4 numbers which are {72,747,6,78}

conclusion: we 4×8 number = 32

Answer: The answer here is x=2

Step-by-step explanation:

This is a linear equation, take 5x to other side ut will change a sign then solve for x.

2x+5=21

2x=21-5

2x=16

Lastly divide by 2 both sides to get 2