Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By romsek

Math Help - Find the roots.

  1. #1
    Junior Member
    Joined
    Mar 2014
    From
    Canada
    Posts
    35

    Find the roots.

    4) Consider the equation H(t) = 16(2)^2t - 10(2)^t + 1. What are its roots? (HINT: Does this look like a quadratic? Perhaps, at least at first, it should be treated like one).

    5) Do the same for Y(x) = 2sin^2x - 3sinx - 2. What is wrong with your solutions?

    So, this is what I've done so far (which may be completely wrong!)

    16(2t)^2 − 10(2)^t + 1 = 0

    u = 2t

    16u^2 − 10u + 1 = 0

    Factored it: (8u-1)(2u-1) = 0
    and then found the zeros: 1, 1/8 and 1/2
    And then I'm not sure about the next part. Do I substitute 2^t for u?

    [8(2^t)-1][2(2^t)-1] = 0
    (16^t - 1)(4^t-1)

    and then how would you find the roots of that? (assuming that I did that correctly...)

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,651
    Thanks
    1062

    Re: Find the roots.

    Quote Originally Posted by eleventhhour View Post
    4) Consider the equation H(t) = 16(2)^2t - 10(2)^t + 1. What are its roots? (HINT: Does this look like a quadratic? Perhaps, at least at first, it should be treated like one).

    5) Do the same for Y(x) = 2sin^2x - 3sinx - 2. What is wrong with your solutions?

    So, this is what I've done so far (which may be completely wrong!)

    16(2t)^2 − 10(2)^t + 1 = 0

    u = 2t

    16u^2 − 10u + 1 = 0

    Factored it: (8u-1)(2u-1) = 0
    and then found the zeros: 1, 1/8 and 1/2
    And then I'm not sure about the next part. Do I substitute 2^t for u?

    [8(2^t)-1][2(2^t)-1] = 0
    (16^t - 1)(4^t-1)

    and then how would you find the roots of that? (assuming that I did that correctly...)

    Thanks!
    you sort of had the right idea but didn't quite pull it off.

    what you want to do is let

    $u=2^t$

    then you can write your original equation as

    $H(u) = 16 u^2 -10 u+1$

    and to find the roots we solve

    $H(u) = 0$

    factoring we get

    $(2u-1)(8u-1)=0$

    $u=\dfrac 1 2 \bigvee u=\dfrac 1 8$ (not sure how you got 1 as a root)($\bigvee$ means OR)

    now

    $u=2^t \Rightarrow t=\ln_2(u)$ so

    $t=\ln_2\left(\dfrac 1 2\right)=-1 \bigvee t=\ln_2\left(\dfrac 1 8\right)=-3$

    so $t=-1 \bigvee t=-3$
    Thanks from eleventhhour
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. How to find roots
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: April 15th 2009, 01:26 AM
  2. Find all roots...
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: January 2nd 2009, 05:00 PM
  3. Find all roots
    Posted in the Algebra Forum
    Replies: 4
    Last Post: August 5th 2008, 11:30 PM
  4. Find the Roots
    Posted in the Algebra Forum
    Replies: 4
    Last Post: April 9th 2008, 08:17 AM
  5. Given 2 imaginary roots find other 2 roots
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 26th 2008, 09:24 PM

Search Tags


/mathhelpforum @mathhelpforum