 After reading this chapter, you should be able to:
1.find the solutions of quadratic equations,
2.derive the formula for the solution of quadratic equations,
3. solve simple physical problems involving quadratic equations.

What are quadratic equations and how do we solve them?

A quadratic equation has the form The solution to the above quadratic equation is given by So the equation has two roots , and depending on the value of the discriminant , , the equation may have real , complex or repeated roots.
If , the roots are complex .
If , the roots are real .
If , the roots are real and repeated.

Example 1

Derive the solution to Solution Dividing both sides by a, , we get Note if a=0, the solution to is Rewrite as Example 2
A ball is thrown down at 50 mph from the top of a building. The building is 420 feet tall. Derive the equation that would let you find the time the ball takes to reach the ground.
Solution

The distance covered by the ball is given by where
u= initial velocity (ft/s)
g= acceleration due to gravity (ft/s2)
t = time (s)

Given we have The above equation is a quadratic equation , the solution of which would give the time it would take the ball to reach the ground. The solution of the quadratic equation is Since t > 0 the valid value of time is .

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