1.) Find a polynomial of degree that has zeros 1, -1 and 1/2 and whose leading coefficient is 3.
2.) Find the value of k such that x+3 is a product of P(x) = x^2 - 10kx + 6

- moongazer

- chestercat

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- anonymous

AT FIRST. do u know what a degree of polynomial means.

- moongazer

\[3x^3+(3x^2/2)−(3x/2)+(3/2)\]
is this correct?

- moongazer

for 1.?

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## More answers

- anonymous

simplify that.

- moongazer

Is my answer correct?

- anonymous

|dw:1343207441484:dw|

- moongazer

how about for no. 2 could you help me?

- anonymous

can u simplify this plz

- anonymous

I DONT THINK YOUR ANSWER IS CORRECT.

- moongazer

ok

- anonymous

FOR NUMBER 2)
do u know factor theorem

- moongazer

could I make \[(x-1/2) -------> (2x-1)\] ????????

- anonymous

|dw:1343207772794:dw|

- anonymous

NOW do u know factor theorem?
and did u get answer for 1)

- moongazer

\[3x^3-(3x^2/2)−3x−(3/2)\]

- moongazer

am I correct now?

- anonymous

NOPE.

- anonymous

BUT U R VERY CLOSE

- moongazer

I'll do it again :)

- anonymous

u just made the sign mistake

- moongazer

could I make (x-1/2) into (2x-1)
because my teacher said there should be no fractions?

- moongazer

@sauravshakya

- anonymous

|dw:1343208282102:dw|

- anonymous

is the correct answer

- moongazer

could I make (x-1/2) into (2x-1) ??????

- anonymous

NOPE because|dw:1343208355724:dw|

- anonymous

but if |dw:1343208386811:dw|

- moongazer

that's what I mean for the second part

- anonymous

because|dw:1343208443188:dw|

- moongazer

isn't that it is zero so that it is possible?

- moongazer

|dw:1343205903760:dw|

- anonymous

IF it is equal to zero then yes u can because |dw:1343208534245:dw|

- moongazer

|dw:1343205945423:dw|

- anonymous

so what?

- moongazer

I got the correct answer :)

- anonymous

and what is that

- moongazer

it mean that there zeroes are both 1/2

- moongazer

so you can use either of the two?

- anonymous

yeah. BUT only in that case. U cannot use this in simplification.

- anonymous

AND NOW SHALL WE BEGIN NO. 2

- moongazer

yup :)

- anonymous

do u know factor theorem.

- moongazer

wait I am trying to solve 1 with (2x-1) :)

- moongazer

I got the same answer :)

- moongazer

I know factor theorem.
If the remainder when dividing P(x) by D(x) is zero, then D(x) is a factor of P(x).
P(x) is any polynomial
D(x) is the divisor
being a factor means it is included in multiplying.

- moongazer

is that correct?
could you improve my definition of factor ?

- anonymous

No u r defination is correct. And can u use this to solve this problem

- moongazer

how
I am confused with the question?

- moongazer

I am thinking of distributing -3 to x

- moongazer

but I can't explain why it is correct :)

- anonymous

your 2 number question simply means that if u divide P(x) by (x+3) then remainder is zero.
|dw:1343209619170:dw|

- moongazer

ohh, I think it also has remainder theorem? :)

- anonymous

YEAH.

- anonymous

now can u

- moongazer

|dw:1343207190855:dw|

- moongazer

I added =0 so that the remainder will be equal to zero making (x+3) a product ?

- anonymous

solve for k

- moongazer

am I correct with my reason?

- anonymous

yeah

- moongazer

k=1/2

- moongazer

@sauravshakya thank you very much for your help :)

- anonymous

U r WELCOME. AND best of luck

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