Question

Statement I Roots of quadratic equation $x^2+3x+5=0$ is $x=\frac{-3\pm i\sqrt{11}}{2}$.
Statement II If $x^2-x+2=0$ is a quadratic equation, then its roots are $\frac{1\pm i\sqrt{7}}{2}$.

• A. Statement 1 is correct
• B. Statement II is correct
• C. Both are correct
• D. Both are incorrect

Answer 1

Answer: (C)

I. Given, $x^2+3x+5=0$
On comparing the given equation with
$a{x}^2+bx+c=0$, we get $a=1,b=3,c=5$
Now, $D=b^2-4ac=(3{)}^2-4\times 1\times 5=9-20=-11<0$
$\Rightarrow x=\frac{-3\pm \sqrt{-11}}{2\times 1}$
$\therefore x=\frac{-3\pm i\sqrt{11}}{2}(\because \sqrt{-1}=i)$
II. Given, $x^2-x+2=0$
On comparing the given equation with
$a{x}^2+bx+c=0$, we get $a=1,b=-1,c=2$
Now, $D=b^2-4ac=(-1{)}^2-4\times 1\times 2=1-8=-7<0$
$\Rightarrow x=\frac{-(-1)\pm \sqrt{-7}}{2\times 1}$
$=\frac{1\pm i\sqrt{7}}{2}(\because \sqrt{-1}=i)$