Question

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