Question

Determine the quadratic equation of each of the following.1.) x=2 and x=3

2.)x=-7 and x=8
3.) x=⅖and x=¾
4.) sum of the root=-2,product of the root=4/7
5.) sum of the root=¼,product of the root=5/4​

Answer 1

To determine quadratic equations from given roots, we use the facts that if x=p and x=q, then the quadratic is (x - p)(x - q) = 0, and if we know the sum and product of roots, it can be formulated using -b/a and c/a, respectively.

Step-by-step explanation:

To determine the quadratic equation given roots, we use the fact that if x=p and x=q are the roots of a quadratic equation, then the equation can be written as (x - p)(x - q) = 0. For a quadratic equation in the form ax²+bx+c=0, if the sum and product of its roots are known, we use the relationships sum of roots = -b/a and product of roots = c/a.

For the roots x=2 and x=3, the quadratic equation is (x - 2)(x - 3) = 0 or x2 - 5x + 6 = 0.

For the roots x=-7 and x=8, the quadratic equation is (x + 7)(x - 8) = 0 or x2 - x - 56 = 0.

For the roots x=2/5 and x=3/4, the quadratic equation is (x - 2/5)(x - 3/4) = 0 or 20x2 - 23x + 6 = 0.

For the sum of roots=-2 and product of roots=4/7, we form the quadratic equation x2 + 2x + 4/7 = 0.

For the sum of roots=1/4 and product of roots=5/4, we form the quadratic equation x2 - 1/4x + 5/4 = 0.