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=-(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=- (b)/(2a) =- (12)/(2\cdot9) =- (2\cdot2\cdot3)/(2\cdot3\cdot3)= - (2)/(3) \\\\Ans.\ The\ discriminant\ is\ \Delta=0`