Question

[8.06] Which polynomial is a perfect square trinomial?

Answer 1

Answer: $4a^2 - 20a + 25$

Step-by-step explanation:

A binomial $ax^2+bx+c=0$ is called perfect square trinomial

if $b^2 = 4ac$ is satisfied.

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

a = 49, b = -28 and c = 16,

$(-28)^2=784$

$4\times 49\times 16 =3136$

$\implies (-28)^2\neq 4(49)(16)$

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

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

a = 4, b = -20 and c = 25,

$(-20)^2=400$

$4\times 4\times 25 =400$

$\implies (-20)^2\neq 4(4)(25)$

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

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

a = 25, b = -20 and c = -16,

$(-20)^2=400$

$4\times 25\times 16 =-1600$

$\implies (-20)^2\neq 4(25)(16)$

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

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

a = 16, b = -24 and c = -9,

$(-24)^2=576$

$4\times 16\times -9 =-576$

$\implies (-24)^2\neq 4(16)(-9)$

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

Answer 2

4a² − 20a + 25.    is the answer.