Write as a product of linear factors: f(x)=x^4-100

When deriving the quadratic formula by completing the square, what expression can be added to both sides of the equation to crea

____ [38]

Answer:

According to steps 2 and 4. The second-order polynomial must be added by $-c$ and $b^{2}$ to create a perfect square trinomial.

Step-by-step explanation:

Let consider a second-order polynomial of the form $a\cdot x^{2} + b\cdot x + c = 0$ , $\forall \,x \in\mathbb{R}$ . The procedure is presented below:

1) $a\cdot x^{2} + b\cdot x + c = 0$ (Given)

2) $a\cdot x^{2} + b \cdot x = -c$ (Compatibility with addition/Existence of additive inverse/Modulative property)

3) $4\cdot a^{2}\cdot x^{2} + 4\cdot a \cdot b \cdot x = -4\cdot a \cdot c$ (Compatibility with multiplication)

4) $4\cdot a^{2}\cdot x^{2} + 4\cdot a \cdot b \cdot x + b^{2} = b^{2}-4\cdot a \cdot c$ (Compatibility with addition/Existence of additive inverse/Modulative property)

5) $(2\cdot a \cdot x + b)^{2} = b^{2}-4\cdot a \cdot c$ (Perfect square trinomial)

According to steps 2 and 4. The second-order polynomial must be added by $-c$ and $b^{2}$ to create a perfect square trinomial.

7 0

3 years ago

Read 2 more answers

Kenyon arrange flowers in a identical bouquets if he had 21 red flowers and 28 yellow flowers what is the greatest number of bou

Contact [7]

84 is the number I came up with.

5 0

4 years ago

05 lc) if x2 = 10, what is the value of x? ±square root of 10 ±square root of 20 ±5 ±20

postnew [5]

$x^2=10\\x=\pm\sqrt{10}$

7 0

4 years ago

Write an equation for the translation of x^2 + y^2 = 49 by 7 units right and 4 units up

Tatiana [17]

Answer:

(x - 7)² + (y - 4)² = 49

Step-by-step explanation:

Given

Equation: x² + y² = 49

Required:

New Equation when translated 7 units right and 4 units up

Taking it one step at a time.

When the equation is translated 7 units right, this implies a negative unit along the x axis.

The equation becomes

(x - 7)² + y² = 49

When the equation is translated 4 units up, this implies a negative unit along the y axis.

(x - 7)² + (y - 4)² = 49

The expression can be further simplified but it's best left in the form of

(x - 7)² + (y - 4)² = 49

8 0

3 years ago

Classify the following data. Indicate whether the data is qualitative or quantitative, indicate whether the data is discrete, co

ruslelena [56]

Answer:

Quantitative.
Discrete.
Interval Scale.

Step-by-step explanation:

The IQ scores are measured numerically. This makes it quantitative data. Quantitative data provide numerical measures which can be used to perform arithmetric operations such as addition, subtraction, multiplication and division. Results from these kind of data can be used to provide meaningful and explanatory results to certain phenomena.
IQ scores are discrete because they are always expressed as integers. that is in whole numbers and not in fractions e.g 100, 120, 60.
The level of measurement is on an interval scale because the difference between values have meanings. Larger values mean higher IQ. for example, the difference in IQ numbers between two people for represents something real.

6 0

4 years ago