Question

Which polynomial is a perfect square trinomial?

Answer 1

Assuming the 2nd one is 4a^2 - 20a +25, it is the one you're looking for. It factors to be (2a-5)^2

Answer 2

Answer:

$4a^2 - 20a+25$

Step-by-step explanation:

Since, for a perfect square trinomial the value of discriminant = 0,

That is, if for a quadratic equation $ax^2+bx+c$

$D=b^2-4ac=0$

Then, $ax^2+bx+c$ is a perfect square trinomial,

For $49x^2 - 28x+16$,

$(-28)^2-4\times 49\times 16=-2352\neq 0$

⇒ $49x^2 - 28x+16$ is not a perfect square trinomial,

For $4a^2 - 20a+25$,

$(-20)^2-4\times 4\times 25=400-400=0$

⇒ $4a^2 - 20a+25$ is a perfect square trinomial,

For $25b^2 - 20b - 16$,

$(-20)^2-4\times 25\times -16=2000\neq 0$

⇒ $25b^2 - 20b - 16$ is not a perfect square trinomial,

For $16x^2 - 24x - 9$,

$(-24)^2-4\times 16\times -9=1152\neq 0$

⇒ $16x^2 - 24x -9$ is not a perfect square trinomial,