What is the nature of roots of the quadratic equation `2x^2-sqrt5x+1=0 ?`

Options

A. two distinct real roots
B. two equal real roots
C. no real roots
D. more than 2 real roots

Answer

C

Explanation

Given equation is `2x^(2)-sqrt(5)x+1=0`
On comparing with `ax^(2)+bx+c=0` we get
`a=2,b=-sqrt(5)` and `c=1`
`:.` Discriminant `D=b^(2)-4ac=(-sqrt(5))^(2)-4xx(2)xx(1)=5-8`
`=-3lt0`
since discriminant is negatice therefore quadratic equation `2x^(2)-sqrt(5)x+1=0` has no real roots i.e. imaginary roots.