Kernel Dorty Don

October 16th, 2015

How to use the quadratic formula

The Khan Academy video on “How to use the quadratic formula” teaches us how to solve for roots or zeroes of quadratic equations by using the quadratic formula.

Definitions: (as given by aleks.com)

Quadratic EquationA quadratic equation (in x ) is an equation of the form ax²+ bx + c = 0 where a, b, and c are numbers (with a≠0 ) and x is a variable. A quadratic equation is a polynomial equation of degree 2.

an example of this, x² - 2x - 3 = 0 is a quadratic equation in x

Formulas: ( you will need to know these )

Quadratic Formula

Example 1:

Before we can start with solving equations, using the quadratic formula we must know it. The quadratic formula is x = [-b ± √(b2 - 4ac)]/2a. We are going to learn how to apply it to problems and solve.

This first example starts us out with, X2 + 4x - 21 = 0

This equation tells us that, a = 1, b = 4 and c = - 21. a = 1 b = 4 c = - 21

All we need to do is take these and plug it into our quadratic formula. ( x = [-b ± √(b2 - 4ac)]/2a)

X = - (4) ± √ (4)2 - 4(1)(-21) / 2 (1)

Now we simplify, X = - 4 ± √ 16 - 4 (1)(-21) / 2

16 + 84

X = -4 ± √ 100 / 2

X = -4 ± 10 / 2

Once we have simplified the most we can, we set our formula up twice, once adding -b + b2 and once subtracting it.

X = -4 + 10 / 2 X = -4 - 10 / 2

X = -4 + 10 / 2 X = -4 - 10 / 2

X = 6 / 2 X = -14 / 2

X = 3 X = -7

These are our answers.

Utilizing the method we used to solve our example problem, you can now use the quadratic formula to solve quadratic equations.