2.3 Forming Quadratic Equations from Given Roots


2.3 Forming Quadratic Equations from Given Roots

Let α and β be the roots of the equation ax2 + bx + c = 0, this means


x = α               or        x = β
x α = 0         or        x β = 0
(x α) (x β) = 0
So,  x2 – (α + β ) x + αβ = 0

Conclusion:

x2 – (sum of roots) x + (product of roots) = 0



Example:
Find the quadratic equation from the respective roots below:
(a) 3, 1
(b) 2, ¼
(c) , ¼
(d) 3m,2m

Solution:



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