Question

1. Solve.

Answer 1

1. using the quadratic formula you get -9+/-sqrt(9^2-4*(1*2))/2*1

 this simplies to x = -9 +/- sqrt(73)/2

x = -0.22799812 and -8.77200187

2.  complex numbers have the letter i with them

 using the quadratic formula

 you get 0 +/- sqrt(0^2-4*(1*24))/2*1

x = -2i sqrt(6) and 2i sqrt(6)

Answer 2

Answer and explanation:

1) Solve : $x^2+9x+2=0$

Applying quadratic formula,

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

Here, a=1 , b=9, c=2

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

$x=\frac{-9\pm\sqrt{81-8}}{2}$

$x=\frac{-9\pm\sqrt{73}}{2}$

$x=\frac{-9+\sqrt{73}}{2},\frac{-9-\sqrt{73}}{2}$

$x=-0.227,-8.772$

2) Given : $x^2+24=0$

To find : What is the solution of the equation when solved over the complex numbers?

Solution :

Quadratic equation, $x^2+24=0$

Subtract 24 both side,

$x^2+24-24=-24$

$x^2=-24$

Taking root both side,

$x=\sqrt{-24}$

$x=\pm 2\sqrt{6}i$

The solution of the equation is $x=2\sqrt{6}i,-2\sqrt{6}i$