what is number of quadratic equation that are unchanged by squaring their roots is

There are four such cases x²  =0 root 0

(x-1)²=0  root 1

x(x+1)=0  roots  0 and 1

x²+x+1=0 roots ω and ω² 

let x² +bx +c=0 ............1

not let another equation whoose roots are square of this equation

so   X=x²   or   x=√X

 put value of x

  X +b√X  +c =0

 or X +c =-b√X

square

   X² +c² +2cX =b²X

   X² +(2c-b²)X + c² =0..................2

root of equation 2 is the square of root of equation 1

both equation will be same if their coefficient are in proportion

1/1  =b/(2c-b²)  =c/c ²

 

b= 2c-b^{2     ................3}            

c=c^{2  ....................3}

 from equation 3  c=0 or 1

 for c =0  b= 0 and -1

  for c=1  b= 1 and -2 

 so four combination are possible

Posted Date: 9/19/2012 6:56:40 AM | Location : United States

Ask an Expert

Related Discussions:- Quadratic equation assignment, Assignment Help, Ask Question on Quadratic equation assignment, Get Answer, Expert's Help, Quadratic equation assignment Discussions

Write discussion on Quadratic equation assignment
Your posts are moderated

Write your message here..

Related Questions

Graph y = cos ( x ) - common graph, Graph y = cos (x) Solution: There ... Graph y = cos (x) Solution: There actually isn't a whole lot to this one.  Given the graph for -4 ? ≤ x ≤ 4 ? . Note that we can put all values of x in cosine (that wo

probability that the card is a 8 or an ace, A standard deck of cards conta... A standard deck of cards contains 52 cards. One card is selected at random. Determine a)    The probability that the card is a 8 or an Ace? b)    The probability that the card is

Linear programming , Use the simplex method to solve the following LP Probl... Use the simplex method to solve the following LP Problem. Max Z = 107x1+x2+2x3 Subject to 14x1+x2-6x3+3x4=7 16x1+x2-6x3 3x1-x2-x3 x1,x2,x3,x4 >=0

Trigonometry, how to work out consumer arithmetic? how to work out consumer arithmetic?

Example of exponential smoothing, Example of Exponential Smoothing ... Example of Exponential Smoothing By using the previous example and smoothing constant 0.3 generate monthly forecasts Months Sales Forecast

Trigonometric functions of two angles, tan45 degrees=tan(90degrees-45degree... tan45 degrees=tan(90degrees-45degrees)

Fraccions, multiply 9/19 times 95/7 multiply 9/19 times 95/7

What is order of operations simplifying expressions, What is Order of Opera... What is Order of Operations Simplifying Expressions? Kevin gives Don directions to his house: "Go left 3 blocks and then go right 2 blocks." Don wasn't paying close attention.

Subtracting fractions, 1+8 1+8

The mean value theorem for integrals, The Mean Value Theorem for Integrals ... The Mean Value Theorem for Integrals If f(x) is a continuous function on [a,b] then here is a number c in [a,b] thus, a ∫ b f(x) dx = f(c)(b -a) Proof Let's begin