SOLUTION: Write the quadratic equation in the form ax^2+bx+c=0 given the following roots. Answer the questions that follow. 1.5 and 9 2.8 and 10 3.6 and 3 4.-8 and -10 5.-3 and 15 6.-9

Algebra ->  Finance -> SOLUTION: Write the quadratic equation in the form ax^2+bx+c=0 given the following roots. Answer the questions that follow. 1.5 and 9 2.8 and 10 3.6 and 3 4.-8 and -10 5.-3 and 15 6.-9      Log On


   

Question 981978: Write the quadratic equation in the form ax^2+bx+c=0 given the following roots. Answer the questions that follow.
1.5 and 9
2.8 and 10
3.6 and 3
4.-8 and -10
5.-3 and 15
6.-9 and 0
7. 2.5 and 4.5
8.-3 and -3
9.-5/6 and -1/6
10. -2/3 and 3/4
Questions:
A.How did you determine the quadratic equation given its root?
B.What mathematics concepts or principles did you apply to arrive at the equation?
C.Are there other ways of getting the quadratic equation given the roots? If there are any,explain and give examples.
D. Compare your answers with those of your classmates. Did you arrive at the same answers? if NOT,explain
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Zero Product principle (x-r)(x-s)=0 for roots r and s. The two multiplied binomials will (usually) give a quadratic trinomial.

Example, #5:
roots or zeros -3 and 15.
%28x-%28-3%29%29%28x-15%29=0
%28x%2B3%29%28x-15%29=0
x%5E2-12x-45=0
system%28a=1%2Cb=-12%2Cc=-45%29

Examples like #7,9,10 can be used to obtain something for a%3C%3E1, because if a is nonzero, it will not affect the truth for a%28x-r%29%28a-s%29=0, for roots r and s.