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mathmath333
 one year ago
Fun question
mathmath333
 one year ago
Fun question

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0looks fun but incomplete.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0add my fb if u wanna get down ;) https://www.facebook.com/ParthKohli

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.0@mathmath333 is this equation really having 3 real roots??

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.2\(\large \color{black}{\begin{align} \text{if}\ p,q,r\ \text{are roots of }\hspace{.33em}\\~\\ 2x^33x^2x1=0 \hspace{.33em}\\~\\ \text{Find}\ (1p)(1q)(1r) \end{align}}\)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.2look at the degree of x , it will have 3 roots

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.0are u talking about 3 real roots???

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.2(xp)(xq)(xr) = 0 multiply that out gives x^2  2x^2 (p + q + r) + 2x (qr + pq + pr)  2pqr = 0 pattern match to original equation so times 2 multiply out (1p)(1q)(1r) and you get same patterns eg p + q + r, (qr + pq + pr) , pqr and pattern match long winded

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.2\(\large \color{black}{\begin{align} \ &2x^33x^2x1=0 \hspace{.33em}\\~\\ &\implies x^3\dfrac{3}{2}x^2\dfrac{x}{2}\dfrac{1}{2}=0 \hspace{.33em}\\~\\ &(xp)(xq)(xq)=x^3\dfrac{3}{2}x^2\dfrac{x}{2}\dfrac{1}{2}\hspace{.33em}\\~\\ &\text{put} \quad x=1 \hspace{.33em}\\~\\ &(1p)(1q)(1q)=1^3\dfrac{3}{2}\times 1^2\dfrac{1}{2}\dfrac{1}{2}\hspace{.33em}\\~\\ \end{align}}\)

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.2aaargh! much better

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.2i will put up another such question

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0This is simply transformation of roots, isn't it?

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0If \(a_1, a_2 , \cdots , a_n\) are the roots of \(p_n(x)=0\) where \(n\) is the degree of the polynomial, then \(1  a_1, 1  a_2, \cdots, 1  a_n\) are the roots of \(p_n(1  x)=0\).

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0\[p'(x) = p(1x) = 2(1x)^3  3(1  x)^2  (1  x)  1\]

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0\[= 2 x^3+3 x^2+x3\]The product of roots of this \(3/2\).
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