Albert Teen YOU ARE LEARNING:     The quadratic formula gives us a method of solving any quadratic equation to a high degree of accuracy.

Another way to solve quadratic equations which do not factorise is to use the quadratic formula.

1

It is used for equations of the form: $ax^2 + bx + c = 0$ where $a$,$b$ and $c$ are known values. When might you use the Quadratic Formula to solve an equation? Let's have a go! Find the values of $x$ for $3x^2 + 11x + 6 = 0$

Remember $x = \dfrac{(- b \pm \sqrt{b^2 - 4ac})}{2a}$ for quadratics in the form $ax^2+bx+c$.

1

What is the value of $a$? 2

What is the value of $b$? 3

What is the value of $c$? 4

Put these values into the formula

$x = \dfrac{(- {\color{#21affb}11} \pm \sqrt{{\color{#21affb}11}^2 - 4\times{\color{#21affb}3}\times{\color{#21affb}6}})}{2\times{\color{#21affb}3}}$

5

Simplify it

$x = \dfrac{(-11 \pm \sqrt{49})}{6}$

6

Remember there are 2 equations here

$x = \dfrac{(-11 {\color{#21affb}+} \sqrt{49})}{6}$ and $x = \dfrac{(-11 {\color{#21affb}-} \sqrt{49})}{6}$

7

We can solve each equation separately

$x = \dfrac{(-11 {\color{#21affb}+} \sqrt{49})}{6}$ can be simplified to $x=\dfrac{-4}{6}=\dfrac{-2}{3}$

8

If $x = \dfrac{(-11 {\color{#21affb}-} \sqrt{49})}{6}$, what is $x$? Nice work! Now use the quadratic formula to solve $3x^2 + 6x + 1 = 0$ Use the quadratic formula to solve $6x^2 + 7x + 2 = 0$ 