Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2006-11-01 03:51:09

Neha
Member
Registered: 2006-10-11
Posts: 173

lead coefficient

find the quadratic equation with a lead corfficient of 1 and whose roots are 2 - 3i and 2 + 3i .

hmm


Live Love Life

Offline

#2 2006-11-01 04:05:06

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: lead coefficient

so, the quadratic is of the form

so plug in the two roots



taking second away from the first


plug back into the first one

so the quadratic is

lets try it out.




The Beginning Of All Things To End.
The End Of All Things To Come.

Offline

#3 2006-11-01 04:26:23

Neha
Member
Registered: 2006-10-11
Posts: 173

Re: lead coefficient

Thanks Luca smile


Live Love Life

Offline

#4 2006-11-03 14:33:02

George,Y
Member
Registered: 2006-03-12
Posts: 1,379

Re: lead coefficient

Veda's(?) Law:
a=-(x1+x2) b=x1 x2

Proof (Incomplete)
If the solution is x1 and x2,
the equation must be able to transform into this form:
(x-x1)(x-x2)=0
<=>
xx-(x1+x2)x+(x1)(x2)=0
so
xx-(2+3i+2-3i)x+(2+3i)(2-3i)=0


X'(y-Xβ)=0

Offline

Board footer

Powered by FluxBB