I'm supposed to factor this:
3z^2-17z+24
I used the quadratic equation, but I'm not sure if that's what I was supposed to use to get the answer. This is how I worked it...
-(-17)+/-sqrt(-17^2-4(3)(24)
---------------------------
2(3)
17+/-sqrt(289-288)
------------------
6
17 sqrt (1) = 17
----------- ----
6 6
is 17/6 correct?
the numbers are quite small, so a few trial and error runs would give you
(x-3)(3x-8)
your method should have given you
(17 +/- 1)/6 = 3 or 8/3
the root of 3 would have given the x-3 factor
the 8/3 would yield the (3x-8) factor
(3z- )(z - )
(3z- 4 )(z -6 ) no
(3z- 6)(z -4 )no
(3z- 8)(z - 3) YES
oh :( okay I definitely used the wrong method then. trial and error is a lot less steps than I used. thank you
To factor the quadratic polynomial 3z^2 - 17z + 24, you can use the quadratic equation as you did. However, the answer you provided is incorrect.
Let's go through the process step by step:
1. Start with the quadratic polynomial in the form: az^2 + bz + c. In this case, a = 3, b = -17, and c = 24.
2. The quadratic equation is given by: z = (-b ± sqrt(b^2 - 4ac))/(2a).
3. Substitute the values of a, b, and c into the quadratic equation to find the values of z:
z = [ -(-17) ± sqrt((-17)^2 - 4(3)(24)) ] / (2 * 3)
Simplifying this expression further:
z = (17 ± sqrt(289 - 288)) / 6
= (17 ± sqrt(1)) / 6
= (17 ± 1) / 6
Now, we have two possible values for z:
1. When z = (17 + 1) / 6 = 18 / 6 = 3.
2. When z = (17 - 1) / 6 = 16 / 6 = 2(2/3).
Thus, the correct factorization of 3z^2 - 17z + 24 is:
3z^2 - 17z + 24 = (z - 3)(z - 2(2/3)).
Please note that you made a mistake when simplifying sqrt(1) as 17/6. The correct values for z are 3 and 2(2/3).