2.2 Roots of Quadratic Equations

Roots of Quadratic Equations

Roots of a quadratic equation are the values of variables/unknowns that satisfy the equation.

Example:
Determine whether 1, 2, and 3 are the roots of the quadratic equation x 2 5 x + 6 = 0 .

Answer:
When x = 1,
x 2 5 x + 6 = 0 ( 1 ) 2 5 ( 1 ) + 6 = 0 2 = 0
x = 1 does not satisfy the equation

When x = 2,
x 2 5 x + 6 = 0 ( 2 ) 2 5 ( 2 ) + 6 = 0 0 = 0
x = 2 satisfies the equation.

When x = 3
x 2 5 x + 6 = 0 ( 3 ) 2 5 ( 3 ) + 6 = 0 0 = 0
x = 3 satisfies the equation.

 Conclusion:
  1. 2 and 3 satisfy the equation x 2 5 x + 6 = 0 , hence there are the roots of the equation.
  2. 1 does not satisfy the equation x 2 5 x + 6 = 0 , hence it is NOT the root of the equation.
Remember : Roots of a quadratic equation are the values of variables/unknowns that satisfy the equation.

Example
(a) Given x = 3 is the root of the quadratic equation x 2 + 2 x + p = 0 , find the value of p.
(b) The roots of the quadratic equation 3 x 2 + h x + k = 0   are -2 and 4. Find the value of h and k.


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