Find the value of b that makes x^(2) +bx+(9)/(4) a perfect square trinomial

Question

Find the value of b that makes
`x^(2) +bx+(9)/(4)` a perfect square trinomial

Answer 1

perfect square trinomial is like

(x+4)^2=x^2+8x+16
they are represented as such
ax^2+bx+c
so to solve for b you do
(√c) times 2=b so

c=9/4
square root=3/2 because 3/2 times 3/2=9/4
(√(9/4)) times 2=(3/2) times 2=6/2=3
so b=3

x^2+3x+(9/4)
if factored, it gives
(x+(3/2))(x+(3/2)) or
(x-(3/2))(x-(3/2))


if this equation is equal to 0 then x=-3/2 or 3/2

the value is 3