Solve by Competing the Square

a.

b.

x2 −8x+ 5 =0

2x2 −5x−9 =0

x =4 ± 11

x =54

±974

9.3 Roots and Coefficients of a Quadratic Function

When given the roots of a quadratic equation we can work backwards to find the quadratic equation.

Example: If you know that your roots are 3 and -4,

that means that and

What would this look like as a factored equation?

How can you get the quadratic equation from there?

x−3 =0 x + 4 =0

So, in general, if we have roots and , we can find the quadratic equation with those roots by simplifying

.

If there are fractional coefficients left, you can multiply both sides by their

to clear the fractions.

If there is only one root, then it is a root and we will use it as both

and .

r1 r2

LCD

x−r1( ) x−r2( ) =0

r1 r2

double

Write the quadratic equation having the given solution set

1. 3,−5{ }

Write the quadratic equation having the given solution set

2. −2

3⎧⎨⎩

⎫⎬⎭

Write the quadratic equation having the given solution set

3. 4 + 2,4 − 2{ }

Write the quadratic equation having the given solution set

4. 2 + 3i, 2 −3i{ }