If P(x) is a cubic polynomial such that P(0)=0 P(2)=-4 and P(x)is positive only when x> 4 find P(x)

Jaxon Hamilton
2022-07-31
Answered

If P(x) is a cubic polynomial such that P(0)=0 P(2)=-4 and P(x)is positive only when x> 4 find P(x)

You can still ask an expert for help

phravincegrln2

Answered 2022-08-01
Author has **19** answers

eventually given that numbers greater than 4 would turn out to be positive, P cubed would have to be positive... and you would have to subtract a multiple of P squared... so far the equation would look like ${P}^{3}-{P}^{2}$ Now just look for a number that would work there (where _ is) with 2 as a given for P and -4 as the answer... ${2}^{3}=8$ $8-(\ast {2}^{2})=-4$ $8-(\ast 4)=-4$

Intomathymnma

Answered 2022-08-02
Author has **5** answers

since P(0)=0 and P(x) is positive only when x > 4 then (0,0) must be a double root with the function staying below the x axis.

since P(x) > 0 when x > 4 then a root must exist at x=4

now you have $y=a{x}^{2}(x-4)$

use the given point (2,-4) to find a

$-4=a{2}^{2}(2-4)$

-4=a (-8)

a=1/2

therefore cubic polynomial is $y=(1/2){x}^{2}(x-4)$

since P(x) > 0 when x > 4 then a root must exist at x=4

now you have $y=a{x}^{2}(x-4)$

use the given point (2,-4) to find a

$-4=a{2}^{2}(2-4)$

-4=a (-8)

a=1/2

therefore cubic polynomial is $y=(1/2){x}^{2}(x-4)$

asked 2021-02-25

Find a polynomial of the specified degree that has the given zeros. Degree 4, zeros -2, 0, 2, 4

asked 2020-10-28

Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3 and zeros 0 and i.

asked 2021-12-18

Part A

For the two vectors in the figure (Figure 1) , find the magnitude of the vector product

Part B

Find the direction of the vector product

Find the direction of the vector product .

Part C

Find the magnitude of

Part D

Find the direction of

asked 2022-06-30

Rewriting $\mathrm{sin}(a+b)=c$

asked 2022-02-28

Verify that

$2{\mathrm{cos}}^{2}x-1=\frac{1-{\mathrm{tan}}^{2}x}{1+{\mathrm{tan}}^{2}x}$

asked 2022-01-17

How do you simplify $(-10i)\left(9i\right)+8$ ?

asked 2021-09-11

Determine the product of the polynomials.

$(4r-1)(7r+2)$