Question

How to find the zeroes of a polynomial? Please give a good explanation.

Answer 1

Answer:

.

Step-by-step explanation:

zeroes of the Polynomial can be find by 3 methods namely :

1. Factorisation method (middle term splitting)

2. Quadratic formula

3. hit and trial method

Explanation :

1. Factorisation Method :

=> In this method we try to split the middle the term in such a way that results as same as the result of the multiplication of extreme left term's coefficient and extreme right term's coefficient.

Example :

${x}^{2} - 2x - 3 = 0$

extreme left term's Coefficient = 1

extreme right term's coefficient = -3

the multiplication result is 1 × -3 = -3

that's Why middle term can be split

${x}^{2} - 3x + x - 3 = 0\\ x(x - 3) + 1(x - 3) = 0 \\ (x - 3)(x + 1) = 0 \\ now \: final \: step \: is \: \\ x - 3 = 0 \: or \: x + 1 = 0 \\ x = 3 \: or \: - 1$

2. Quadratic Formula

=> this is generally used when middle term can't be split

let's take an example :

${x}^{2} - 2x - 3 \\ \\ a = 1\: \: \: \: b = - 2 \: \: \: c = - 3 \\ \\ now \: quadratic \: formula \: is \: \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ lets \: find \: out \: d \\ \\ d = {b}^{2} - 4ac \\ \\ ({ - 2})^{2} - 4 \times 1 \times ( - 3) = 16 \\ \\ x = \frac{ - b + - \sqrt{d} }{2a} \\ \\ = \frac{ - ( - 2) + - \sqrt{16} }{2(1)} \\ \\ x = \frac{2 + 4}{2} \\ \\ or \: \frac{2 - 4}{2} \\ x = 3 \: or \: - 1$

Here is the complete solution of your question..