Question 234934: For this problem I need to use the discriminate to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. It is not necessary to find the roots; just determine the number and types of solutions. This is a word problem
A designer attempts to arrange the characters of his artwork in the form of a square grid with equal numbers of rows and columns, but finds that 24 characters are left out. When he tries to add one more row and column, he finds that he has 25 too few characters. Find the number of characters used by the designer.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! The answer is 600.
The equations used are:
x^2 = y - 24
(x+1)^2 = y + 25
You set:
y = x^2 + 24
y = (x+1)^2 - 25
Then you set:
x^2 + 24 = (x+1)^2 - 25
because they both equal y so they are equal to each other.
You solve for x.
The x^2 cancels out as shown below:
(x+1)^2 - x^2 = 49
This becomes:
x^2 + 2x + 1 - x^2 = 49
The x^2 cancels out so the equation becomes:
2x + 1 = 49
Subtract 49 from both sides to get:
2x - 48 = 0
The general form of a quadratic equation is:
ax^2 + bx + c
This means that:
a = 0
b = 2
c = -48
The discriminant is b^2 - 4ac
This becomes 2^2 - 4*0*-48 which becomes:
4
Unfortunately, since a = 0, the whole quadratic formula becomes:
-b +/- sqrt (b^2-4ac) / 2a
Since a = 0, this means the solution is undefined.
I'm not sure what they were trying to tell you here.
Your equation is a straight line, not a quadratic equation, because the x^2 term canceled out.
You have one solution and one solution only, but it is not a quadratic equation.
The answer becomes x = 24
24^2 = 576 + 24 = 600
25^2 = 625 - 25 = 600
The discriminant is described here !!!!!
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