Question

If D = 0 then the value of each root of the quadratic equation ax2

+ bx + c = 0 is​

Answer 1

$distriminant \: (d) = b {}^{2} - 4ac \\ = 0 \\ so \\ {b}^{2} = 4ac \\ then \: c = \frac{ {b}^{2} }{4a} \\ put \: the \: value \: in \\ a {x}^{2} + bx + c = 0 \\ a {x}^{2} + bx + \frac{ {b}^{2} }{4a} = 0 \\ divide \: a \: to \: both \: side \\ \frac{a {x}^{2} }{a} + \frac{bx}{a} + ({ \frac{b}{2a} )}^{2} = \frac{0}{a} \\ this \: form \: an \: algebraic \: identity \\ {(z+ y)}^{2} = {z}^{2} + 2zy + {y}^{2} \\ where \: z = {x}^{} \\ y = \frac{b}{2a} \\ {x}^{2} + 2 \times \frac{b}{2a}x + (\frac{b}{2a} ) {}^{2} = 0 \\ {(x + \frac{b}{2a}) }^{2} = 0 \\ x = \frac{ + }{} \frac{b}{2a}$