Question 66485
WHICH ONE OF THE FOLLOWING IS TRUE? 
a. The equation (2x-3)2 = 25 is equivalent to 2x-3=5
b. Every quadratic equation has two distinct numbers in its solution set
c. The equation 3y-1=11 and 3y-7=5 are equivalent
d. The equation ax2 + c = 0, a is not equal 0, cannot be solved by the quadratic formula 
**NOTE in both a and d the 2 is meant to be the exponent


a.  (2x-3)^2=25  take sqrt of both sides
 2x-3=5
True



b. Lets look at the standard form for a quadratic equation ax^2+bx+c=0
The quadratic formula is: x=(-b+or-sqrt(b^2-4ac))/2a
If a=0, then the formula blows apart
If (b2-4ac)<0, then the solution set is imaginary
If b^2=4ac, then we only have one solution, (-b)
Example:x^2+2x+1 We can factor this quadratic (x+1)(x+1)
x=-1


So the answer is False.  


c.  3y-1=11  add 1 to both sides

3y-1+1=11+1
3y=12

3y-7=5  add 7 to both sides
3y-7+7=5+7
3y=12
True



d.   ax^2+c =0


 Using the quadratic formula x=(-b+or-sqrt(b^2-4ac))/2a

x=(-0+or-sqrt(0^2-4ac))/2a simplifying:

x=(+or-sqrt(-4ac))/2a
x=(+or-(2sqrt(-ac)/2a
x=(+or-sqrt(-ac))/a


False---it can be solved by the quadratic formula and if a or c is negative, then we should have real roots


Hope this helps------ptaylor