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4-1.Complex numbers
medium
निम्नलिखित समीकरणों में से प्रत्येक को हल कीजिए
$\sqrt{2} x^{2}+x+\sqrt{2}=0$
A
$\frac{-1 \pm \sqrt{7} i}{2 \sqrt{2}}$
B
$\frac{-1 \pm \sqrt{7} i}{2 \sqrt{2}}$
C
$\frac{-1 \pm \sqrt{7} i}{2 \sqrt{2}}$
D
$\frac{-1 \pm \sqrt{7} i}{2 \sqrt{2}}$
Solution
The given quadratic equation is $\sqrt{2} x^{2}+x+\sqrt{2}=0$
On comparing the given equation with $a x^{2}+b x+c=0$
We obtain $a=\sqrt{2}, b=1,$ and $c=\sqrt{2}$
Therefore, the discriminant of the given equation is
$D=b^{2}-4 a c=1^{2}-4 \times \sqrt{2} \times \sqrt{2}=1-8=-7$
Therefore, the required solutions are
$\frac{-b \pm \sqrt{D}}{2 a}=\frac{-1 \pm \sqrt{-7}}{2 \times \sqrt{2}}=\frac{-1 \pm \sqrt{7} i}{2 \sqrt{2}} \quad[\sqrt{-1}=i]$
Standard 11
Mathematics
