Select the correct answer.

Evaluate the function for the given values to determine if the value is a root. p(−2) = p(2) = The value is a root of p(x).

bija089 [108]

Note: Since you missed to mention the the expression of the function $p(x)$ . After a little research, I was able to find the complete question. So, I am assuming the expression as $p(x)=x^4-9x^2-4x+12$ and will solve the question based on this assumption expression of $p(x)$ , which anyways would solve your query.

Answer:

As

$p\left(-2\right)=0$

Therefore, $x=-2$ is a root of the polynomial $p(x)=x^4-9x^2-4x+12$

As

$p\left(2\right)=-16$

Therefore, $x=2$ is not a root of the polynomial $p(x)=x^4-9x^2-4x+12$

Step-by-step explanation:

As we know that for any polynomial let say $p(x)$ , $c$ is the root of the polynomial if $p(c)=0$ .

In order to find which of the given values will be a root of the polynomial, $p(x)=x^4-9x^2-4x+12$ , we must have to evaluate $p(x)$ for each of these values to determine if the output of the function gets zero.

So,

Solving for $p\left(-2\right)$

$p(x)=x^4-9x^2-4x+12$

$p\left(-2\right)=\left(-2\right)^4-9\left(-2\right)^2-4\left(-2\right)+12$

$\mathrm{Simplify\:}\left(-2\right)^4-9\left(-2\right)^2-4\left(-2\right)+12:\quad 0$

$\left(-2\right)^4-9\left(-2\right)^2-4\left(-2\right)+12$

$\mathrm{Apply\:rule}\:-\left(-a\right)=a$

$=\left(-2\right)^4-9\left(-2\right)^2+4\cdot \:2+12$

$\mathrm{Apply\:exponent\:rule}:\quad \left(-a\right)^n=a^n,\:\mathrm{if\:}n\mathrm{\:is\:even}$

$=2^4-2^2\cdot \:9+8+12$

$=2^4+20-2^2\cdot \:9$

$=16+20-36$

$=0$

Thus,

$p\left(-2\right)=0$

Therefore, $x=-2$ is a root of the polynomial $p(x)=x^4-9x^2-4x+12$ .

Now, solving for $p\left(2\right)$

$p(x)=x^4-9x^2-4x+12$

$p\left(2\right)=\left(2\right)^4-9\left(2\right)^2-4\left(2\right)+12$

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$p\left(2\right)=2^4-9\cdot \:2^2-4\cdot \:2+12$

$p\left(2\right)=2^4-2^2\cdot \:9-8+12$

$p\left(2\right)=2^4+4-2^2\cdot \:9$

$p\left(2\right)=16+4-36$

$p\left(2\right)=-16$

Thus,

$p\left(2\right)=-16$

Therefore, $x=2$ is not a root of the polynomial $p(x)=x^4-9x^2-4x+12$ .

Keywords: polynomial, root

Learn more about polynomial and root from brainly.com/question/8777476

#learnwithBrainly

7 0

2 years ago

Read 2 more answers

What is the value of x in the equation -6 x = 5 x + 22? A. -22 B. -2 C. 2 D. 22

Novosadov [1.4K]

Answer:

B. -2

Step-by-step explanation:

-6x = 5x + 22

Put the like terms together, so subtract 5x from the right side. This will result in the new equation, -11x = 22

Now, divide by -11. This will result in the final equation, x = -2

4 0

2 years ago

Read 2 more answers

Find the surface area of the figure below. Round to the nearest tenth if necessary.

Contact [7]

Answer:

173.4 cm^2

Step-by-step explanation:

Surface area of the cone=pi*r*l+pi*r^2=pi*(4)*(9.8+4)=173.4 cm^2

6 0

1 year ago

Please help

Montano1993 [528]

Answer:

M = 2x² - (ax/3) + by

B = - 3x²y + (xy³/3) - cy

Step-by-step explanation:

Equation 1 is

2x² - (1/3)ax + by - M = 0

M = 2x² - (ax/3) + by

Equation 2

3x²y - (1/3)xy³ + cy + B = 0

B = - 3x²y + (xy³/3) - cy

Hope this Helps!!!

7 0

2 years ago

“a railroad bridge spans a gorge 40 feet wide and connects two cliffs at heights of 98 and 158 feet above the bottom of the gorg

VMariaS [17]

Answer:

Height above the bottom gorge is 113 feet

Step-by-step explanation:

The width of the gorge = 40 feet

The height of the higher cliff = 158 feet

The height of the lower cliff = 98 feet

The length of the bridge = √((158-98)² + 40²) = 72.11 feet

The slope of the bridge = (158-98)/40 = 1.5

The length of 1/4 of the bridge from the lower cliff =72.11 - 3/4×72.11 = 18.03 feet

The angle of inclination of the bridge = tan⁻¹(1.5) = 56.31°

The height above the bottom at 3/4 from the higher cliff = The height above the bottom at 1/4 from the lower cliff = 98+ 18.03×sin(56.31 ) = 113 feet

Which can also be found directly from the heights of the two cliffs knowing that 3/4 from the higher cliff = 1/4 from the lower cliff giving;

Height above the bottom gorge = 98 + 1/4×(158 - 98) = 113 feet.

8 0

2 years ago