Question

find the zeros of P(x)=
6x^{4}-7x^{3}+56x^{2}-63x+18. include
descartes rule of signs,upper bound, etc. thanks

Answer #1

**The function is**

**Apply Descartes rule of signs, from the polynomial find
the number of sign changes.**

**Positive Root Case:**

**There are four sign changes in P(x) from + to -, - to +,
+ to - and - to + implies there are maximum 0,2,4 positive
roots**

**Negative Root Case:**

**That is**

**There are NO sign changes in P(x) implies there are NO
negative roots**

**---**

**From Rational zeroes, roots are of the form
where p is factor of constant term and q is factor of the leading
coefficient. Factors of 18 are 1,2,3,6,9,18 and factors of 6 are
1,2,3,6**

**Since there are no negative roots implies possible roots
are**

**Find where f(root)=0 implies**

**Hence, there are 2 positive roots implies
are factors of P(x). Divide polynomial P(x) by the above two
factors using long division**

**Hence, P(x) can be written as**

**Roots are**

Use Descartes' Rule of Signs to determine how many positive and
how many negative real zeros the polynomial can have. Then
determine the possible total number of real zeros. (Enter your
answers as comma-separated lists.) P(x) = 6x3 − 5x2 + 8x − 1

1. Find all rational zeros of the polynomial, and then find the
irrational zeros, if any. Whenever appropriate, use the Rational
Zeros Theorem, the Upper and Lower Bounds Theorem, Descartes' Rule
of Signs, the Quadratic Formula, or other factoring techniques.
(Enter your answers as comma-separated lists. Enter all answers
including repetitions. If an answer does not exist, enter DNE.)
P(x) = 2x4 + 7x3 − 6x2 − 7x + 4 rational zeros x = irrational zeros
x =
2. A...

p(x)= 3x4+7x3- 40x2- 134x- 40
find all real zeros

f(x) =+x3−3x2+ 9x+ 13. Find an upper and a lower bound on the
real zeros of(x).

Find the least upper bound and the greatest lower bound for the
two polynomials:
a) p(x) = x4 - 3x2 - 2x + 5
b) p(x) = -2x5 + 5x4 + x3 - 3x
+ 4

A polynomial P is given.
P(x) = x4 − 16
(a) Find all zeros of P, real and complex. (Enter your
answers as a comma-separated list. Enter all answers including
repetitions.)
x =
(b) Factor P completely.
P(x) =

find the upper bound of the LTE (euler)
2x'+2/3 x = 4x^2
and the interval for t is [0,1].

p(x)= 2x4-9x3-23x2+81x+45 find
all zeros of the polynomial

find all real zeros if the function P(x)=2x^4-x^3-4x^2+10x-4
i know all possible zeros are + or - 1, +- 1/2, +-2, +-4
im not sure how to do this and show the work

Find a polynomial? P(x) with real coefficients having a degree?
4, leading coefficient 22?, and zeros 44minus?ii and 33ii.
?P(x)equals= nothing

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 10 minutes ago

asked 16 minutes ago

asked 39 minutes ago

asked 48 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago