Question

If $(a,4)$ lies on the graph of $f\left(x\right)=x^2-5x^2-3x$ then the value of $a$ is

Answer 1

Given equation

$f\left(x\right)=y=x^2-5x^2-3x$

point $(x,y)=(a,4)$

$\therefore \Rightarrow 4=a^2-5a^2-3a$

$\Rightarrow 4=-4a^2-3a$

$\Rightarrow 4a^2+3a+4=0$

$\Rightarrow a=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{-3\pm \sqrt{9-64}}{8}$

$=\frac{-3\pm i\sqrt{55}}{8}$

$=\frac{-3+i\sqrt{55}}{8}$, $\frac{-3-i\sqrt{55}}{8}$.