SOLUTION: 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 equati

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
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
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

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