Question

Discriminant of 9x^2+12x+4=0

Answer 1

$9x^2+12x+4=0\\\\(3x)^2+2\cdot3x\cdot2+2^2=0\\\\(3x+2)^2=0\iff3x+2=0\\\\3x=-2\ \ \ /:3\\\\x=-\frac{2}{3}\\\\-------------------------------\\\\(a+b)^2=a^2+2ab+b^2$

Answer 2

$the\ discriminant\ of\ ax^2+bx+c=0:\ \ \ \ \Delta=b^2-4\cdot b\cdot c \\---------------------------\\9x^2+12x+4=0\ \ \ \Rightarrow\ \ \ \Delta=12^2-4\cdot9\cdot4=144-144=0\\\\\Delta=0\ \ \ \Rightarrow\ \ \ x_0=- \frac{b}{2a} =- \frac{12}{2\cdot9} =- \frac{2\cdot2\cdot3}{2\cdot3\cdot3}= - \frac{2}{3} \\\\Ans.\ The\ discriminant\ is\ \Delta=0$