A perfect square trinomial can be represented by a square model with equivalent length and width. Which polynomial can be represented by a perfect square model? a. x2 – 6x + 9b. x2 – 2x + 4c. x2 + 5x + 10d. x2 + 4x + 16
Accepted Solution
A:
The correct answer is [tex]A) x^2 - 6x + 9[/tex]
In fact, this is a trinomial of the form [tex]ax^2-bx+c[/tex], whose solutions are given by [tex]x_{1,2}= \frac{-b\pm \sqrt{b^2 -4ac} }{2a}[/tex] Using this formula for the trinomial of the problem, we find: [tex]x1,2= \frac{6 \pm \sqrt{6^2-4\cdot 1\cdot 9}}{2} =3[/tex] we see that this trinomial has two coincident solutions (x=3 with multiplicity 2). This means that it can be rewritten as a perfect square, in the following form: [tex](x-3)^2[/tex]