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In details

Factored form


Consider the equation ax2 + bx + c = 0. Putting The in evidence we get:

Then we can write:

Therefore, the factored form of the equation ax2 + bx + c = 0 is:

a. (x - x '). (x - x ") = 0

Examples:

  • Write in factored form the equation x2 - 5x + 6 = 0.
    Solution:Calculating the roots of equation x2 - 5x + 6 = 0, we get x1= 2 and x2= 3.
    Where a = 1, x1= 2 and x2= 3, the factored form of x2 - 5x + 6 = 0 can be written as follows: (x-2). (X-3) = 0

  • Write in factor form the equation 2x2 - 20x + 50 = 0.
    Solution:
    Calculating the roots of the 2x equation2 - 20x + 50 = 0, we get two real roots equal to 5. Being a = 2, x1= x2= 5, the factored form of 2x2 - 20x + 50 = 0 can be written as follows:
    2. (x - 5) (x - 5) = 0 or 2. (x - 5)2=0

  • Write in the factored form the equation x2 + 2x + 2 = 0.
    Solution:As the , the equation has no real roots.
    Therefore, this equation has no factored form in IR.

Next: Beamed Equations