SOLUTION: Question 1: How many solutions exist for a quadratic equation? How do we determine whether the solutions are real or complex? Question 2: Translate the following i

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Question 192564: Question 1:

How many solutions exist for a quadratic equation? How do we determine whether the solutions are real or complex?

Question 2:
Translate the following into a quadratic equation, and solve it: The length of a rectangular garden is four times its width; if the area of the garden is 196 square meters, what are its dimensions?

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
D=discriminant =b%5E2-4ac ax%5E2%2Bbx%2Bc=0
:
if D>0 2 reals
if D=0 1 real
if D<0 2 complex roots
:
let L be the length and W width A=area
:
A=L*W.........eq 1
L=4W..........eq 2
A=196.........eq 3
:
take L's value from eq 2 and A's value from eq 3 and plug them into eq 1
:
196=4W(W)
:
4W%5E2-196=0
:
W%5E2-49=0divided by 4
:
W%5E2=49
:
W=7
:
L=4(7)=28