The quadratic equation 2x2 – √5x + 1 = 0 has


The quadratic equation 2x2 – √5x + 1 = 0 has

(a) two distinct real roots

(b) two equal real roots

(c) no real roots

(d) more than 2 real roots


(c) Given equation is $2 x^{2}-\sqrt{5} x+1=0$.

On comparing with $a x^{2}+b x+c=0$, we get

$a=2, b=-\sqrt{5}$ and $c=1$

$\therefore$ Discriminant, $\quad D=b^{2}-4 a c=(-\sqrt{5})^{2}-4 \times(2) \times(1)=5-8$


Since, discriminant is negative, therefore quadratic equation $2 x^{2}-\sqrt{5} x+1=0$ has no real roots i.e., imaginary roots.

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