Quadratic equations

Solve a quadratic equation using the quadratic formula

The general form of a quadratic equation is where a, b, c are constants (generally integers).

A quadratic equation with real coefficients can have none, one or two distinct real roots. To find them, use the Quadratic Formula:

$\fs2x^2-5x+6\;=\;0\;\Rightarrow\;x=\frac{5\pm\sqrt{(-5)^2-4(1)(6)}}{2\;1}\;\Rightarrow\;x=\frac{5\pm\sqrt{25-24}}{2}\;\Rightarrow\;x=\frac{5\pm1}{2}$

$\fs2x_1=\frac{5+1}{2}=\frac{6}{2}=3\;\;\;\;x_2=\frac{5-1}{2}=\frac{4}{2}=2$

Solve $\fs1-3x^2-5x-9\;=\;0$

No solution
One solution x=
Two solutions x₁= x₂=