CBSE Class 10 Answered
Sir Can you explain me how to find zeros of polynomials by giving any example or explaining it?
Asked by | 17 Jun, 2011, 12:00: AM
Expert Answer
Follow this procedure step by step:
- If solving an equation, put it in standard form with 0 on one side and simplify.
- Know how many roots to expect.
- If youre down to a linear or quadratic equation (degree 1 or 2), solve by inspection or the quadratic formula.
Then go to step 7. - 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 cant, go to step 6.
- Divide by your factor. This leaves you with a new reduced polynomial whose degree is 1 less. For the rest of the problem, youll work with the reduced polynomial and not the original. Continue at step 3.
- If you cant find a factor or root, turn to numerical methods.
Then go to step 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 |
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 | 17 Jun, 2011, 03:46: PM
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