Quadratic equations

Quadratic Equation

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:

or factorise it.

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

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

Factorise x²+6x-8=0
We require to numbers that multiply together to give 8 and add together to give 6.
So the numbers are 2 and 4.
Hence x²+6x-8=(x-2)(x-4)

Solve $\fs1-3x^2-54x-243=0$

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