Answer to Question #307954 in Calculus for Niu_bi

Question

F(x) = x² + 9x - 4

Answer 1

Solution

$f(x)=x^2+9x-4$

To solve this quadratic equation $x^2+9x-4=0$, we use the quadratic formula

x = \frac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\

$a=1, b=9, c=-4$

x = \frac{{ - \left( 9 \right) \pm \sqrt {{{\left( 9 \right)}^2} - 4\left( 1 \right)\left( { - 4} \right)} }}{{2\left( 1 \right)}}\

x = \frac{{ - 9 \pm \sqrt {81 + 16} }}{2}\

x = \frac{{ - 9 + \sqrt {97} }}{2},\,\,\,\,x = \frac{{ - 9 - \sqrt {97} }}{2}\

$x=0.424, x=-9.424$

Hence the two solutions are

$x=0.424, x=-9.424$

The same has been shown in the following plot.