Question

Which polynomial is a perfect square trinomial?

49x2 − 28x 16
4a2 − 20a 25
25b2 − 20b − 16
16x2 − 24x − 9

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

`4a^2 - 20a+25`

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* 49* 16=-2352\\eq 0`

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

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

`(-20)^2-4* 4* 25=400-400=0`

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

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

`(-20)^2-4* 25* -16=2000\\eq 0`

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

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

`(-24)^2-4* 16* -9=1152\\eq 0`

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