Determine-the-coordinates-where-the-function-f-x-ax-2-bx-c-admits-a-local-point-

Question Number 100391 by Ar Brandon last updated on 26/Jun/20

D etermine the coordinates where the function f (x) = {ax}^{2} + bx + c

admits a local point .

Answered by MJS last updated on 26/Jun/20

{a x}^{2} + b x + c = x

{a x}^{2} + (b - 1) x + c = 0

x = \frac{1 - b}{2 a} \pm \frac{\sqrt{{(b - 1)}^{2} - 4 a c}}{2 a}

{(b - 1)}^{2} - 4 a c = D

\Rightarrow {\begin{cases} D < 0 \Rightarrow no local point \\ D = 0 \Rightarrow 1 local point \\ D > 0 \Rightarrow 2 local points \end{cases}

Commented by Ar Brandon last updated on 26/Jun/20

Thanks Sir��