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I have the equation- $$(-3p)^2 + 4(4p+1)$$

how do I make it have equal roots? cause I don't think it's possible but must be, can someone please help

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    That's not an equation. An equation mus have an equal sign in it. And if you want to think of it as a polynomial in $p$, then you cannot "make it" do anything. It is a specific, fixed, polynomial; the discriminant is $16^2 - 16\times 9 = 16(7)\neq 0$ (unless you are working over a field of characteristic $2$ or $7$, I guess...)2012-02-28
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    it is =0 (I think) but i just need it to go into 2 bracets2012-02-28
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    "is =0" doesn't make sense to me; and I don't know what "go into 2 bracets" means.2012-02-28
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    @Siobhan What is your mothertongue? It seems you have some difficulties in explaining what you need.2012-02-28
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    the equation is (-3p)squared +4(4p+1) = 0 and i need it to be go into two brackets like x squared +2 would go into (x+2) (x+1)2012-02-28
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    what dose mothertongue mean???2012-02-28
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    You can't go from an expression that involves $p$ but no $x$ to an expression that involves $x$ but no $p$ by performing nothing but algebraic manipulations. Your post is completely confusing. Please post the **entire** problem (with context), if you want someone to help you.2012-02-28
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    @Siobhan: What is your native language? It is clear that you do not speak English as a first language. What *is* your first language? In what language is the problem you are facing written in?2012-02-28
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    you know what never mind I'm bad at explaining things, thanks for trying to help but never mind. Sorry for wasting your time2012-02-28
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    btw it is English!2012-02-28
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    @Siobhan: You won't get good at explaining things unless you keep trying! People are having difficulty understanding what problem you are trying to solve and are pushing you to express yourself better (that's an important step to improving your problem solving skills). Part of your difficulty with the problem is likely the fact that you don't fully understand what is being asked of you, so trying to articulate the problem better will help you with this problem (and others as well).2012-02-28
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    @AndréNicolas' guess gets my vote for what was originally being asked of the OP. Also Siobhan, 1 - "getting to go into two brackets" is called **factoring**. 2 - $$x^2 + 2$$ does NOT factor into $$(x + 1)(x + 2)$$. You should distribute/"FOIL" this out to check...2012-02-28
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    oops and thanks :P2012-02-28
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    @Siobhan: Suppose that instead of what you wrote down, the actual problem is to solve $(-3p)^2-4(4p+1)=0$. This equation simplifies to $9p^2-16p -4=0$, which can be rewritten as $(9p+2)(p-2)=0$. Then the roots are $-2/9$ and $2$. Your post put us in the middle of a problem. Can you restate the problem exactly as it was asked?2012-02-28

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If I understand correctly all you need is to factorize this polynomial. You get by solving the 2nd order equation $9p^2+16p+4=0$: $$9p^2+16p+4=-\frac{1}{9}(-9p+2\sqrt{7}-8)(9p+2\sqrt{7}+8)$$

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    thank that is almost what i need to do but the answer is much simpler (I'm only doing higher maths). Buts thank for the help2012-02-28
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    If "the answer is much simpler", then the question is not what you asked. Could it have been $(-3p)^2 + 4(3p+1)$?2012-02-28
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    Ok can we ust accept that I've written it wrong and leave it be. Thank again for all the help, but I'm a lost cause I'm afraid2012-02-28
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    You're not a lost cause! You just need to be a bit more careful, and also learn the correct terminology.2012-02-28
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A root of an polynomial is a value for the variable that makes the polynomial equal to zero. So you can't "make it have equal roots", it has the roots that it has and they won't change.

The roots happen to be $\dfrac {2} {9}\left(-4+\sqrt {7}\right)$ and $\dfrac {2} {9}\left( -4-\sqrt {7}\right)$. These are not equal. There is a different kind of problem where some of the numbers in your polynomial are unknown and you are expected to find a value for those that will give multiple roots that are equal, but that would be a different problem.