MHB 5.t.11 find x for the imaginary factors

  • Thread starter Thread starter karush
  • Start date Start date
  • Tags Tags
    Factors Imaginary
karush
Gold Member
MHB
Messages
3,240
Reaction score
5
$\textbf{5.t.11 }$ McKinley HS

Find x for $f(x)=0 \quad 5+i\quad 5-i\quad $
$\begin{array}{rl}
\textsf{factored} &f(x)=(x-1)[x-(5+i))(x-(5-i)]\\
\textsf{foil} &x^2-x(5+i)-x(5-i)+(5-i)^2\\
\textsf{expand} &x^2-5x-xi-5x+xi+25-2i+i^2 \\
\textsf{simplify} &x^2-10x+26\\
\textsf{observation } &(x-1)=0,\quad x=1\\
\textsf{quadratic formula} &=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\
&=\dfrac{-(10)\pm\sqrt{(10)^2-4(1)(26)}}{2(1)}\\
&=\dfrac{-1\pm\sqrt{100-96}}{2}
=\dfrac{-10\pm2i}{2}=5\pm i
\end{array}$

can't seem to get the errors out of this;)
 
Mathematics news on Phys.org
karush said:
$\textbf{5.t.11 }$ McKinley HS

Find x for $f(x)=0 \quad 5+i\quad 5-i\quad $
$\begin{array}{rl}
\textsf{factored} &f(x)=(x-1)[x-(5+i))(x-(5-i)]\\
\textsf{foil} &x^2-x(5+i)-x(5-i)+(5-i)^2\\
\textsf{expand} &x^2-5x-xi-5x+xi+25-2i+i^2 \\
\textsf{simplify} &x^2-10x+26\\
\textsf{observation } &(x-1)=0,\quad x=1\\
\textsf{quadratic formula} &=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\
&=\dfrac{-(10)\pm\sqrt{(10)^2-4(1)(26)}}{2(1)}\\
&=\dfrac{-1\pm\sqrt{100-96}}{2}
=\dfrac{-10\pm2i}{2}=5\pm i
\end{array}$

can't seem to get the errors out of this;)
First: Your problem didn't state that f(1) = 0.

Second: [math]f(x)=(x-1)[x-(5+i))(x-(5-i))][/math] gives the zeros 1, 5 - i, and 5 + i but is a cubic. You left out the (x - 1) factor and got a quadratic. You never stated f(x).

Third: The last term in the quadratic expansion is [math](5 + i)(5 - i) = 25 - i^2 = 26[/math]

(Fourth: 25 + i^2 = 25 - 1 = 24. Your wrote 26 in the quadratic formula, which is correct but your work would have set c = 24 and given the wrong answer.)

Fifth: b = -10, not b = 10.

Sixth: [math]100 - 4 \cdot 26 = -4[/math], not 4.

You need to drink more coffee when you are doing these.

-Dan
 
ok thanks
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.

Similar threads

Replies
2
Views
1K
Replies
3
Views
1K
Replies
8
Views
1K
Replies
5
Views
1K
Replies
1
Views
1K
Replies
7
Views
2K
Replies
1
Views
974
Replies
6
Views
1K
Back
Top