Question

Solve the equation $x^2+3x+5=0$

Answer 1

Step 1: Given
$x^2+3x+5=0$

Step 2:Check nature of roots
$D=b^2-4ac,a=1,b=3,c=5$
$\Rightarrow D=9-20=–11<0$
$\therefore D$ is negative
$\therefore$ Roots are imaginary,so we can use the quadratic formula.

Step 3: Using quadratic formula
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
By putting the values of $a,b,c$
$x=\frac{-3\pm \sqrt{9-4\left(1\right)\left(5\right)}}{2}$
$x=\frac{-3\pm \sqrt{-11}}{2}$
$x=\frac{-3\pm \sqrt{11}i}{2}$
The values of $x$ are $\frac{-3+\sqrt{11}i}{2},\frac{-3-\sqrt{11}i}{2}$