## moongazer 3 years ago 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

1. sauravshakya

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

2. moongazer

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

3. moongazer

for 1.?

4. sauravshakya

simplify that.

5. moongazer

6. sauravshakya

|dw:1343207441484:dw|

7. moongazer

how about for no. 2 could you help me?

8. sauravshakya

can u simplify this plz

9. sauravshakya

10. moongazer

ok

11. sauravshakya

FOR NUMBER 2) do u know factor theorem

12. moongazer

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

13. sauravshakya

|dw:1343207772794:dw|

14. sauravshakya

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

15. moongazer

\[3x^3-(3x^2/2)−3x−(3/2)\]

16. moongazer

am I correct now?

17. sauravshakya

NOPE.

18. sauravshakya

BUT U R VERY CLOSE

19. moongazer

I'll do it again :)

20. sauravshakya

u just made the sign mistake

21. moongazer

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

22. moongazer

@sauravshakya

23. sauravshakya

|dw:1343208282102:dw|

24. sauravshakya

25. moongazer

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

26. sauravshakya

NOPE because|dw:1343208355724:dw|

27. sauravshakya

but if |dw:1343208386811:dw|

28. moongazer

that's what I mean for the second part

29. sauravshakya

because|dw:1343208443188:dw|

30. moongazer

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

31. moongazer

|dw:1343205903760:dw|

32. sauravshakya

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

33. moongazer

|dw:1343205945423:dw|

34. sauravshakya

so what?

35. moongazer

I got the correct answer :)

36. sauravshakya

and what is that

37. moongazer

it mean that there zeroes are both 1/2

38. moongazer

so you can use either of the two?

39. sauravshakya

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

40. sauravshakya

AND NOW SHALL WE BEGIN NO. 2

41. moongazer

yup :)

42. sauravshakya

do u know factor theorem.

43. moongazer

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

44. moongazer

I got the same answer :)

45. 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.

46. moongazer

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

47. sauravshakya

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

48. moongazer

how I am confused with the question?

49. moongazer

I am thinking of distributing -3 to x

50. moongazer

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

51. sauravshakya

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

52. moongazer

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

53. sauravshakya

YEAH.

54. sauravshakya

now can u

55. moongazer

|dw:1343207190855:dw|

56. moongazer

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

57. sauravshakya

solve for k

58. moongazer

am I correct with my reason?

59. sauravshakya

yeah

60. moongazer

k=1/2

61. moongazer

@sauravshakya thank you very much for your help :)

62. sauravshakya

U r WELCOME. AND best of luck