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  • The quadratic equation 2x^{2}-\sqrt{5}x+1=0 has (A) two distinct real roots (B) two equal real roots (C) no real roots (D) more than 2 real roots

The quadratic equation 2x^{2}-\sqrt{5}x+1=0  has

(A) two distinct real roots                                 (B) two equal real roots

(C) no real roots                                                (D) more than 2 real roots

Answers (1)

(C) no real roots

\text{Here the given quadratic equation is }2x^{2}-\sqrt{5}x+1=0

\text{ Compare with }ax^{2}+bx+c=0 \text{ where } a \neq 0
 \\a=2, b=\sqrt{5},c=1\\ b^{2}-4ac=(-\sqrt{5})^{2}-4(2)(1\\ =5-8=-3

b^{2}-4ac<0

\text{Hence the equation }2x^{2}-\sqrt{5}x+1=0\text{ has no real roots.}  

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infoexpert24

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