Is f(x) = -16x^2 + 24x + 16 a perfect square trinomial?

Question

anonymous · Answer

@Hero @jim_thompson5910 @satellite73 @mathmate @mathmale

jim_thompson5910 · Answer

-16x^2 + 24x + 16 is in the form ax^2 + bx + c

jim_thompson5910 · Answer

so a = -16, b = 24, c = 16

solomonzelman · Answer

4x²+6x+4   (when you factor out of 4)

anonymous · Answer

Ok @SolomonZelman , so it isn't a perfect square trinomial?

jim_thompson5910 · Answer

plug those values into the discriminant formula

D = b^2 - 4ac

D = 24^2 - 4*(-16)*16

D = 1600

Because this discriminant is 1600, and not 0, this means that we don't have a perfect square. The discriminant has to be 0 for it to be a perfect square trinomial.

Recall that having a discriminant of 0 means you have exactly one solution. Something like (x-2)^2 = 0 has exactly one solution.

solomonzelman · Answer

yes, but since 1600 =40², you trinomial IS factor-able (into integers)

anonymous · Answer

Thanks @jim_thompson5910 and @SolomonZelman :)

anonymous · Answer

id give u a medal @SolomonZelman if i could, but i can only give 1. sorry :( but thank you:)