Mathematics, 02.07.2019 02:30 kami2006

Factor f(x)=x4-x3-7x2+13x-6 completely. then sketch the graph

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Answer from: QueenYaya

ANSWER TO QUESTION 1

f(x)=(x-2)(x+3)(x-1)^2 .

EXPLANATION

The function given to us is,

f(x)=x^4-x^3-7x^2+13x-6

According to rational roots theorem,

$\pm1,\pm2,\pm3,\pm6$ are possible rational zeros of

f(x)=x^4-x^3-7x^2+13x-6 .

We find out that,

f(-3)=(-3)^4-(-3)^3-7(-3)^2+13(-3)-6

f(-3)=81+27-63-39-6

f(-3)=6-6

f(-3)=0

Also

f(2)=(2)^4-(2)^3-7(2)^2+13(2)-6

f(2)=16-8-28+26-6

f(2)=6-6

f(2)=0

This implies that

x-2 and x+3 are factors of

f(x)=x^4-x^3-7x^2+13x-6 and hence (x-2)(x+3)=x^2+x-6 is also a factor.

We perform the long division as shown in the diagram.

Hence,

f(x)=(x-2)(x+3)(x-1)^2 .

ANSWER TO QUESTION 2

Sketching the graph

We can see from the factorization that the roots

x=2 and x=-3 have a multiplicity of 1, which is odd. This means that the graph crosses the x-axis at this intercepts.

Also the root x=1 has a multiplicity of 2, which is even. This means the graph does not cross the x-axis at this intercept.

Now we determine the position of the graph on the following intervals,

$x\le -3$

f(-4)=(-4)^4-(-4)^3-7(-4)^2+13(-4)-6

$f(-4)=150\:0$

$-3\le x \le 1$

$f(0)=-6\:$

$1\le x\le 2$

$f(1.5)=-0.56\:$

$x \ge 2$

$f(3)=24\:0$

We can now use these information to sketch the function as shown in diagram

Factor f(x)=x4-x3-7x2+13x-6 completely. then sketch the graph

Answer from: Quest

a) one student is chosen from classroom a, then a student is chosen from classroom b.

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b. this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes. this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes. this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes. this makes them dependent events.

Answer from: Quest

the answer is a

step-by-step explanation:

39.00 x 24 = total installment price

carrying installment price - cash price

needed to save the .00/

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Factor f(x)=x4-x3-7x2+13x-6 completely. then sketch the graph...