moongazer
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
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sauravshakya
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AT FIRST. do u know what a degree of polynomial means.
moongazer
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\[3x^3+(3x^2/2)−(3x/2)+(3/2)\]
is this correct?
moongazer
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for 1.?
sauravshakya
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simplify that.
moongazer
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Is my answer correct?
sauravshakya
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|dw:1343207441484:dw|
moongazer
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how about for no. 2 could you help me?
sauravshakya
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can u simplify this plz
sauravshakya
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I DONT THINK YOUR ANSWER IS CORRECT.
moongazer
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ok
sauravshakya
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FOR NUMBER 2)
do u know factor theorem
moongazer
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could I make \[(x-1/2) -------> (2x-1)\] ????????
sauravshakya
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|dw:1343207772794:dw|
sauravshakya
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NOW do u know factor theorem?
and did u get answer for 1)
moongazer
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\[3x^3-(3x^2/2)−3x−(3/2)\]
moongazer
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am I correct now?
sauravshakya
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NOPE.
sauravshakya
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BUT U R VERY CLOSE
moongazer
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I'll do it again :)
sauravshakya
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u just made the sign mistake
moongazer
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could I make (x-1/2) into (2x-1)
because my teacher said there should be no fractions?
moongazer
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@sauravshakya
sauravshakya
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|dw:1343208282102:dw|
sauravshakya
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is the correct answer
moongazer
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could I make (x-1/2) into (2x-1) ??????
sauravshakya
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NOPE because|dw:1343208355724:dw|
sauravshakya
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but if |dw:1343208386811:dw|
moongazer
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that's what I mean for the second part
sauravshakya
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because|dw:1343208443188:dw|
moongazer
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isn't that it is zero so that it is possible?
moongazer
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|dw:1343205903760:dw|
sauravshakya
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IF it is equal to zero then yes u can because |dw:1343208534245:dw|
moongazer
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|dw:1343205945423:dw|
sauravshakya
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so what?
moongazer
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I got the correct answer :)
sauravshakya
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and what is that
moongazer
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it mean that there zeroes are both 1/2
moongazer
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so you can use either of the two?
sauravshakya
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yeah. BUT only in that case. U cannot use this in simplification.
sauravshakya
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AND NOW SHALL WE BEGIN NO. 2
moongazer
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yup :)
sauravshakya
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do u know factor theorem.
moongazer
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wait I am trying to solve 1 with (2x-1) :)
moongazer
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I got the same answer :)
moongazer
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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
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is that correct?
could you improve my definition of factor ?
sauravshakya
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No u r defination is correct. And can u use this to solve this problem
moongazer
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how
I am confused with the question?
moongazer
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I am thinking of distributing -3 to x
moongazer
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but I can't explain why it is correct :)
sauravshakya
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your 2 number question simply means that if u divide P(x) by (x+3) then remainder is zero.
|dw:1343209619170:dw|
moongazer
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ohh, I think it also has remainder theorem? :)
sauravshakya
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YEAH.
sauravshakya
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now can u
moongazer
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|dw:1343207190855:dw|
moongazer
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I added =0 so that the remainder will be equal to zero making (x+3) a product ?
sauravshakya
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solve for k
moongazer
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am I correct with my reason?
sauravshakya
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yeah
moongazer
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k=1/2
moongazer
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@sauravshakya thank you very much for your help :)
sauravshakya
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U r WELCOME. AND best of luck