1.

The roots of the equation \(\rm \sqrt 2x^2 -x + \dfrac{1}{\sqrt{2}}=0\) are:1. imaginary2. real and equal3. real and distinct4. None of the above

Answer» Correct Answer - Option 1 : imaginary

Concept:

Let us consider the standard form of a quadratic equation, ax2 + bx + c =0

Discriminant = D = b2 – 4ac

  • If the Discriminant > 0 then the roots are real and distinct.
  • If the Discriminant = 0 then the roots are real and equal.
  • If the Discriminant < 0 then the roots are Imaginary.

 

Calculation:

\(\rm \sqrt 2x^2 -x + \dfrac{1}{\sqrt{2}}=0\)

⇒ 2x2 - √2x + 1 = 0

Comparing this with the standard form ax2 + bx + c = 0, we get a = 2, b = -√2 and c = 1.

∴ D = b2 - 4ac

= (-√2)2 - 4 × 2 × 1

= 2 - 8 = - 6 

D < 0

Hence roots are imaginary. 


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