Sir Can you explain me how to find zeros of polynomials by giving any example or explaining it?

Asked by  | 17th Jun, 2011, 12:00: AM

Expert Answer:

Follow this procedure step by step:

  1. If solving an equation, put it in standard form with 0 on one side and simplify.  
  2. Know how many roots to expect. 
  3. If you’re down to a linear or quadratic equation (degree 1 or 2), solve by inspection or the quadratic formula.  
    Then go to step 7.
  4. Find one rational factor or root. This is the hard part, but there are lots of techniques to help you.  If you can find a factor or root, continue with step 5 below; if you can’t, go to step 6.
  5. Divide by your factor. This leaves you with a new reduced polynomial whose degree is 1 less.   For the rest of the problem, you’ll work with the reduced polynomial and not the original. Continue at step 3.
  6. If you can’t find a factor or root, turn to numerical methods.  
    Then go to step 7.
  7. If this was an equation to solve, write down the roots. If it was a polynomial to factor, write it in factored form, including any constant factors you took out in step 1.
 

Example: Solve 5x² + 6x + 1 = 0

Coefficients are:   a = 5, b = 6, c = 1
     
Quadratic Formula:   x = [ -b ± ?(b2-4ac) ] / 2a
     
Put in a, b and c:   x = [ -6 ± ?(62-4×5×1) ] / (2×5)
     
Solve:   x = [ -6 ± ?(36-20) ]/10
    x = [ -6 ± ?(16) ]/10
    x = ( -6 ± 4 )/10
    x = -0.2 or -1

 

5x^2+6x+1

Answer: x = -0.2 or x = -1

 

And you can see them on this graph.

 

Check -0.2: 5×(-0.2)² + 6×(-0.2) + 1
= 5×(0.04) + 6×(-0.2) + 1
= 0.2 -1.2 + 1
= 0
Check -1: 5×(-1)² + 6×(-1) + 1
= 5×(1) + 6×(-1) + 1
= 5 - 6 + 1
= 0

Answered by  | 17th Jun, 2011, 03:46: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.