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# 2.2 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 ${x}^{2}-5x+6=0$ .

When x = 1,
$\begin{array}{l}{x}^{2}-5x+6=0\\ \left(1{\right)}^{2}-5\left(1\right)+6=0\\ 2=0\end{array}$
x = 1 does not satisfy the equation

When x = 2,
$\begin{array}{l}{x}^{2}-5x+6=0\\ \left(2{\right)}^{2}-5\left(2\right)+6=0\\ 0=0\end{array}$
x = 2 satisfies the equation.

When x = 3
$\begin{array}{l}{x}^{2}-5x+6=0\\ \left(3{\right)}^{2}-5\left(3\right)+6=0\\ 0=0\end{array}$
x = 3 satisfies the equation.

Conclusion:
1. 2 and 3 satisfy the equation ${x}^{2}-5x+6=0$ , hence there are the roots of the equation.
2. 1 does not satisfy the equation ${x}^{2}-5x+6=0$ , 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 ${x}^{2}+2x+p=0$ , find the value of p.
(b) The roots of the quadratic equation $3{x}^{2}+hx+k=0$   are -2 and 4. Find the value of h and k.

### 1 thought on “2.2 Roots of Quadratic Equations”

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