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True [87]
3 years ago
15

What polynomial has roots of -6, 1, and 4 ​

Mathematics
2 answers:
Taya2010 [7]3 years ago
7 0

Answer:

C

Step-by-step explanation:

Given the roots of the polynomial are x = - 6, x = 1 and x = 4 the the factors are

(x + 6), (x - 1) and (x - 4)

The polynomial is the product of the factors, that is

f(x) = a(x - 1)(x - 4)(x + 6) ← a is a multiplier

let a = 1 and expand the first pair of factors

f(x) = (x² - 5x + 4)(x + 6)

     = x(x² - 5x + 4) + 6(x² - 5x + 4) ← distribute both parenthesis

     = x³ - 5x² + 4x + 6x² - 30x + 24 ← collect like terms

f(x) = x³ + x² - 26x + 24 → C

Lelu [443]3 years ago
5 0

Answer:

x^3 + x^2 - 26x + 24.

Step-by-step explanation:

Knowing the roots we can immediately write it in factor form as follows:

f(x) = (x + 6)(x - 1)(x - 4).

Note that when  f(x) = 0 each of the factors can be zero and , for example, when  x + 6 = 0 then x = -6.

We now expand the  expression:

(x + 6)(x - 1)(x - 4)

= (x + 6)(x^2 - 4x - 1x + 4)

= (x + 6)(x^2 - 5x + 4)

= x(x^2 - 5x + 4) + 6(x^2 - 5x + 4)

= x^3 - 5x^2 + 4x + 6x^2 - 30x + 24    Adding like terms:

= x^3 + x^2 - 26x + 24.  (Answer).

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PLEASE PLEASE HELP ME I REALLY NEED HELP
Gekata [30.6K]

Answer:

(a) yes it does

(b) the rate is constant because the rate of change (slope) is the same throughout the function.

(c) The rate, or rate of change, is -1/2.

y1 - y2/x1-x2

4 - 2/3 - 9

2/-6

-1/2

7 0
3 years ago
Which are acute, obtuse, or right?
qaws [65]
5,7 and 8 are right angles, and 6 is an acute angle this is because of u look at 9 and 10 you can see a little box looking thing under the h and if u do that to all of them 5, 7 and 8 can fit the little box but 6 you can’t because it is an acute angle. Hope this helped!
8 0
3 years ago
Among 500 freshmen pursuing a business degree at a university, 311 are enrolled in an economics course, 243 are enrolled in a ma
Allushta [10]

Solution :

Let A = Economics, B = Mathematics

n(A) = 311, n(B) = 243, $n(A \cap B) = 135$

a). So, $n(A \cup B) = n(A) +n(B) - n(A \cap B)$

                     = 311 + 243 - 135

                     = 419

b). n(A only) = 311 - 135

                   = 176

     n(B only) = 243 - 135

                   = 108

Exactly one of these two courses

  $=\frac{176+108}{500}$

  = 0.568

c). Neither economics nor mathematics

    $=\frac{500-419}{500} $

  $=\frac{81}{500}$

 = 0.162

7 0
3 years ago
Assume Cylinder A and Cone B are the same height and the bases have the same radius. If A has a volume of 18π cm3, what is the v
disa [49]

Answer:

Option A  V_B=19\ cm^3

Step-by-step explanation:

The volume of a cone is:

V_B = \pi\frac{hr ^ 2}{3}

The volume of a cylinder is:

V_A = \pi(r ^ 2)h

Both figures have the same height h and the same radius r.

The volume of the cylinderV_A = 18\pi\ cm ^ 3

We want to find the volume of the cone.

Then, we find r and h:

V_A = 18\pi = \pi(r ^ 2)h

We simplify.

V_A = 18 = (r ^ 2)h

Then the product of (r ^ 2)h = 18.

We substitute this in the cone formula and get:

V_B =\frac{\pi}{3}(18)\\\\V_B = \frac{18}{3}\pi\\\\V_B=19\ cm^3

8 0
3 years ago
Read 2 more answers
Multiply:<br><br> (-4 + i)(-1 + 5i)
Olegator [25]

Answer:

( - 4 + i) ( - 1 + 5i) \\  = 4 - 20i - 1i + 5 {i}^{2}  \\  = 4 - ( -21i )+ 5i {}^{2}

3 0
3 years ago
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