Question

State the nature of the given quadratic equation $\sqrt{2}{x}^2-\frac{3}{\sqrt{2}}x+\frac{1}{\sqrt{2}}=0$

• A. Real and Distinct roots
• B. Real and equal roots
• C. Imaginary roots
• D. None of the Above

Answer 1

The correct option is A Real and Distinct roots

In $a{x}^2+bx+c=0$
Find Discriminant $D=b^2-4ac$
If $D=0$, roots are real and equal
If $D>0$, roots are real and not equal
If $D<0$, roots are not real roots

$D=(-\frac{3}{\sqrt{2}}{)}^2-(4\left)\right(\sqrt{2}\left)\right(\frac{1}{\sqrt{2}})$
$=\frac{9}{2}-4=\frac{1}{4}$

Therefore, roots of given equation are real and not equal.