Question

Write a quadratic equation with integer coefficients and the given numbers as solutions.

1. 2 and 5
2. 0 and 5
3. -3/4 and 2
4. 1/2 and 1/3

Answer 1

1.) f(x) = x*x - 7x + 10

2.) f(x) = x*x - 5x

3.) f(x) = 4*x*x - 5x - 6

4.) f(x) = 6*x*x -5x + 1

Explanation:

1.) 2 and 5 (x -2)(x - 5) = f(x) = x*x - 7x + 10

2.) 0 and 5 f(x) = x*(x -5) = x*x - 5x

3.) -3/4 and 2 (x + 3/4)(x -2) = x*x - (5/4) x - 3/2,

need integers f(x) = 4xx - 5x - 6

4.) 1/2 and 1/3 (x - 1/2)(x - 1/3) = f(x)

x*x - 1/3 x - 1/2 x + 1/6

xx - 5/6 x + 1/6

6 xx - 5x + 1