Albert Teen
powered by
Albert logo

YOU ARE LEARNING:

The Quadratic Formula

The Quadratic Formula

The Quadratic Formula

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

This is the quadratic formula

It is used for equations of the form: ax2+bx+c=0ax^2 + bx + c = 0 where aa,bb and cc are known values.

When might you use the Quadratic Formula to solve an equation?

Let's have a go! Find the values of xx for 3x2+11x+6=03x^2 + 11x + 6 = 0

Remember x=(b±b24ac)2ax = \dfrac{(- b \pm \sqrt{b^2 - 4ac})}{2a} for quadratics in the form ax2+bx+cax^2+bx+c.

1

What is the value of aa?

2

What is the value of bb?

3

What is the value of cc?

4

Put these values into the formula

x=(11±1124×3×6)2×3x = \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=(11±49)6 x = \dfrac{(-11 \pm \sqrt{49})}{6}

6

Remember there are 2 equations here

x=(11+49)6 x = \dfrac{(-11 {\color{#21affb}+} \sqrt{49})}{6} and x=(1149)6 x = \dfrac{(-11 {\color{#21affb}-} \sqrt{49})}{6}

7

We can solve each equation separately

x=(11+49)6 x = \dfrac{(-11 {\color{#21affb}+} \sqrt{49})}{6} can be simplified to x=46=23x=\dfrac{-4}{6}=\dfrac{-2}{3}

8

If x=(1149)6 x = \dfrac{(-11 {\color{#21affb}-} \sqrt{49})}{6}, what is xx?

Nice work! Now use the quadratic formula to solve 3x2+6x+1=03x^2 + 6x + 1 = 0

Use the quadratic formula to solve 6x2+7x+2=06x^2 + 7x + 2 = 0