The document discusses quadratic equations and their roots. It provides examples of writing the quadratic equation given the roots. Specifically: 1) It shows how to write the quadratic equation x^2 - 8x + 12 = 0 given the roots are 2 and 6. 2) It shows how to write the quadratic equation 2x^2 - 9x + 4 = 0 given the roots are 4 and 1/2. 3) The key steps are finding the sum and product of the roots, and using those values to write the quadratic equation in the form x^2 - (sum of roots)x + (product of roots) = 0.

1. Ms. G. Martin

2. The quadratic equation ax2 + bx + c = 0 can be written as
x2 – (x1 + x2)x + (x1 . x2) = 0.

3. 1. Factor: (x – 2)(x – 6)
Roots: x = 2 and x = 6
Equation: X2 – 8x + 12 = 0
2. Factor: (x + 5)(x – 3)
Roots : x = -5 and x = 3
Expression: x2 + 2x - 15

4. Example 1.
Find the quadratic equation whose roots are 2 and 6.
Steps Solution
1. Find the sum of the roots of
the indicated quadratic equation
Let x1 = 2 and x2 = 6
x1 + x2 = 2 + 6 = 8
2. Find the product of the roots of
the indicated quadratic equation.
x1 . x2 = 2 . 6 = 12

5. Steps Solution
3. We know that ax2 + bx + c = 0 can
be written as
x2 – (x1 + x2)x + (x1 . x2) = 0.
x2 – (x1 + x2)x + (x1 . x2) = 0.
x2 – (8)x + (12) = 0
x2 – 8x + 12 = 0
So, the quadratic equation whose roots are 2 and 6 is x2 – 8x + 12 = 0

6. Example 2.
Find the quadratic equation whose roots are 4 and
1
2
.
Steps Solution
1. Find the sum of the roots of the
indicated quadratic equation
Let x1 = 4 and x2 =
1
2
x1 + x2 = 4 +
1
2
=
9
2
2. Find the product of the roots of
the indicated quadratic equation.
x1 . x2 = (4)(
1
2
) =
4
2
= 2

7. Steps Solution
3. We know that ax2 + bx + c = 0 can be
written as
x2 – (x1 + x2)x + (x1 . x2) = 0.
x2 – (x1 + x2)x + (x1 . x2) = 0.
x2 – sum(
9
2
)x + product(2) = 0
x2 –
9
2
x + 2 = 0
4. Multiply the result in step 3 by 2.
x2 –
9
2
x + 2 (2)
2x2 – 9x + 4 = 0
So, the quadratic equation whose roots are 4 and
1
2
is 2x2 – 9x + 4 = 0