How To Solve Polynomial Equations

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 When P (x) = 0         … (1)
 Where P (x) is a polynomial expression then the equation (1) is known as a polynomial equation with variable x of        highest power n where n = 0, 1, 2, 3, …, n.
 

Examples of polynomial expression: -
·         x^2 + 8 x + 16 = 0
·         (x – 1) ( x^3 – 6 x^2 + 9 x) = 0
·         x^2 – x = 0
·         x^5 + 6 x^4 + 4 x^2 – 4 x + 8 = 0


Question 1: - Solve the following polynomial equation and find the value of x.
 
Solution: -
i)             Factorize the L.H.S. polynomial expression
              X^2 + 8 x + 16
             = x^2 + 2 * x * 4 + (4)^2
             = (x + 4) ^2
 
ii)          Now write the L.H.S.  expression equal to zero then solve and find the value of x.
            (x + 4) ^2 = 0
            X + 4 = 0
            X = - 4
Therefore x = - 4



Question 2: - If (x – 1) ( x^3 – 6 x^2 + 9 x) = 0, find x.
 
Solution: -
            (x – 1) (x^3 – 6 x^2 + 9 x) = 0
            (x – 1) {x (x ^2 – 6 x + 9)} = 0
            X (x – 1) (x ^2 – 2 * x * 3 + 3 ^2) = 0
            X (x – 1) (x ^2 – 3) ^2 = 0
Therefore x = 0
X – 1 = 0,       hence x = 1
(x ^2 – 3) ^2 = 0, or, x – 3 = 0,         hence x = 3
Answer: - Therefore x = 0, 1, 3, 3
 

 

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