Answer:

1. x² - 25 = 0

2. x² - 17 + 72 = 0

3. x² - x - 6 = 0

4. 6x² - 7x + 2 = 0

5. 10x² - 27x + 18 = 0

Step-by-step explanation:

This is the first way to write the quadratic equations from the roots.

1. x - 5 =0 and x + 5 =0

(x - 5) (x + 5)

by FOIL Method

x² - 25 = 0

2. x - 8 = 0 and x - 9 = 0

(x - 8) (x - 9)

by FOIL Method

x² - 17 + 72 = 0

3. (x + 2) = 0 and (x - 3) = 0

(x + 2) (x - 3)

by FOIL Method

x² - x - 6 = 0

The other way to write the quadratic equations from the roots.

4. Sum: 2/3 + 1/2 = 7/6

Remember- The formula for the sum of the roots is -b/a so,

a = 6 b = -7 c = ?

Product: (2/3) (1/2) = 2/6

The formula for the product of the roots is c/a so,

a = 6 b = -7 c = 2

Equation: 6x² - 7x + 2 = 0

5. (x - 3/2) = 0 and (x - 6/5) = 0

(x - 3/2) (x - 6/5)

By FOIL Method

x² - 27/10x + 9/5 = 0

or

10x² - 27x + 18 = 0