Question

use discriminant to determine the number and type of solutions of the equation:
4x^2-12x=-9
choose correct statement:
a. the equation has one real number solution b. the equation has two complex number solutions c. the equation has two real number solutions

Answer 1

first write
\[4x^2-12x+9=0\] then compute
\[b^2-4ac\] with
\[a=4,b=-12,c=9\]you get
\[(-12)^2-4\times 4\times 9=0\] which means there is one real solution

Answer 2

it also means
\[4x^2-12x+9\] is a perfect square. it is
\[(2x-3)^2\]