[8.06] Which polynomial is a perfect square trinomial?
49x2 − 28x + 16
4a2 − 20a + 25
25b2 − 20b − 16
16x2 − 24x − 9
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,
\((-28)^2=784\)
\(4\times 49\times 16 =3136\)
\(\implies (-28)^2 eq 4(49)(16)\)
Thus, \(49x^2 - 28x + 16\) is not a perfect square trinomial.
For \(4a^2 - 20a + 25\)
a = 4, b = -20 and c = 25,
\((-20)^2=400\)
\(4\times 4\times 25 =400\)
\(\implies (-20)^2 eq 4(4)(25)\)
Thus, \(4a^2 - 20a + 25\) is a perfect square trinomial.
For \(25b^2 - 20b - 16\)
a = 25, b = -20 and c = -16,
\((-20)^2=400\)
\(4\times 25\times 16 =-1600\)
\(\implies (-20)^2 eq 4(25)(16)\)
Thus, \(25b^2 - 20b - 16\) is not a perfect square trinomial.
For \(16x^2 - 24x - 9\)
a = 16, b = -24 and c = -9,
\((-24)^2=576\)
\(4\times 16\times -9 =-576\)
\(\implies (-24)^2 eq 4(16)(-9)\)
Thus, \(16x^2 - 24x - 9\) is not a perfect square trinomial.