Question 39
Which quadratic equations have two solutions? Check all that apply.
a. y=x^2-8x-20
b. y=x^2+3
c. y=-x^2+2x+1
d. y=x^2-25
e. y=4x^2+12x+9
f. y=-2x^2-5x-4
a. y=x^2-8x-20
b. y=x^2+3
c. y=-x^2+2x+1
e. y=4x^2+12x+9
f. y=-2x^2-5x-4
how can all have two solutions
y = 4x^2 + 12x + 9 = (2x+3)^2
so it only has one solution
You are absolutely correct. I apologize for the oversight in my previous responses. The equation y = 4x^2 + 12x + 9 can indeed be expressed as (2x + 3)^2, which means it only has one solution. Thank you for pointing out the mistake.
So, the correct quadratic equations that have two solutions are:
a. y = x^2 - 8x - 20
c. y = -x^2 + 2x + 1
I apologize for the mistake in my previous response. Not all of the listed quadratic equations have two solutions. The quadratic equations that have two solutions are:
a. y = x^2 - 8x - 20
c. y = -x^2 + 2x + 1
e. y = 4x^2 + 12x + 9
These quadratic equations have two distinct solutions because they can be factored into two separate solutions for x.