## 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. moongazer

My answer for no. 1 is \[3x^3 -( 3x^2/2) - 3x + (3/2)\] but my teacher said there should be no fractions

2. lgbasallote

then multiply all the terms by 2(the denominator) to get rid of the fraction

3. moongazer

but the leading coefficient will not be 3???

4. moongazer

@saifoo.khan

5. moongazer

could you help me?

6. saifoo.khan

|dw:1343106002554:dw|

7. moongazer

What does it mean by leading coefficient?

8. saifoo.khan
9. moongazer

10. saifoo.khan

you did a mistake in multiplying.

11. saifoo.khan

(x-1)(x+1)(x-1/2) = 0 try again.

12. moongazer

I'll do it again :)

13. saifoo.khan

Sure.

14. moongazer

I did (x-1)(x+1)(2x-1) = 0 is it the same as (x-1)(x+1)(x-1/2) = 0 ??

15. saifoo.khan

yup.

16. moongazer

I got\[x^3+( x^2/2) -(x/2)+(1/2)\] I checked it twice :)

17. moongazer

@saifoo.khan is this correct?

18. saifoo.khan

Now this is correct!! :D

19. saifoo.khan

NOw get rid of 2 in the denominators, multiply the whole expression by 2.

20. moongazer

\[2x^3 + x^2 - x + 1\]

21. moongazer

How will I make it into 3?

22. saifoo.khan

Are decimals allowed?

23. moongazer

he said there is no fractions

24. saifoo.khan

SInce your teacher said NO FRACTIONS.

25. saifoo.khan

:D

26. moongazer

that's why I am confused :) or maybe I misheard him :)

27. saifoo.khan

Possibly..

28. saifoo.khan

We can multiply the equation by 1.5 to make the leading coef as 3. :D

29. moongazer

maybe he is referring to (2x-1) and (x-1/2)

30. saifoo.khan

2x-1 and x-1/2 is same.

31. saifoo.khan

are* same.

32. moongazer

so my answer I think is \[3x^3 + (3x^2/2) - (3x/2) + (3/2)\] that's the only expression I can have to make the leading coefficient equal to 3

33. moongazer

is that correct?

34. saifoo.khan

3x^3 + 1.5x^2 - 1.5x + 1.5 NO FRACTIONS!!! :D

35. moongazer

lol, I'll just include that to my answer :)

36. moongazer

how about for the second one ?

37. saifoo.khan
38. saifoo.khan

That question looks like a challenge!!

39. moongazer

it should be P(x) = x^2 - 10kx + 6

40. moongazer

41. saifoo.khan

Find the value of k such that x+3 is a product of P(x) = x^2 - 10kx + 6 (-3)^2 - 10k(-3) + 6 = 0 9 + 30 k + 6 = 0

42. moongazer

I got k = 1/2 but why did you made x into -3?

43. saifoo.khan

Because since it's a product of it, the remainder is 0.

44. saifoo.khan

So we insert the factor and set the equation = 0.

45. moongazer

Thanks, I understand it :)

46. saifoo.khan

Great. Welcome.