The quadratic equation 2x2 - sqrt(5)x + 1 = 0 has

Option c: No real roots. Solution: For a quadratic equation of the form ax2 + bx + c = 0 , the nature of the roots is determined by its discriminant, denoted by Delta or D : D = b2 - 4ac In the given equation, 2x2 - sqrt(5)x + 1 = 0 , we identify the coefficients: a = 2, b = -sqrt(5), c = 1 Now, calculate the discriminant: D = (-sqrt(5))2 - 4 × 2 × 1 D = 5 - 8 D = -3 Since the discriminant is negative ($D Hence, Option C is the correct answer.

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

The correct answer is Option c: No real roots. For a quadratic equation of the form $ax^2 + bx + c = 0$, the nature of the roots is determined by its discriminant, denoted by $\Delta$ or $D$: $$D = b^2 - 4ac$$ In the given equation, $2x^2 - \sqrt{5}x + 1 = 0$, we identify the coefficients: $$a = 2, \quad b = -\sqrt{5}, \quad c = 1$$ Now, calculate the discriminant: $$D = (-\sqrt{5})^2 - 4 \times 2 \times 1$$ $$D = 5 - 8$$ $$D = -3$$ Since the discriminant is negative ($D Hence, **Option C** is the correct answer.

EquationsPYQ May 25Question 4006 of 155

All Questions

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

Options

ATwo distinct real roots

BTwo equal real roots

CNo real roots

DMore than two real roots

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Correct Answer

✅ Option c — No real roots

All Options:

ATwo distinct real roots
BTwo equal real roots
CNo real roots
DMore than two real roots

Detailed Solution & Explanation

For a quadratic equation of the form

\displaystyle ax^2 + bx + c = 0

, the nature of the roots is determined by its discriminant, denoted by

\displaystyle \Delta

\displaystyle D

D = b^2 - 4ac

In the given equation,

\displaystyle 2x^2 - \sqrt{5}x + 1 = 0

, we identify the coefficients:

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

Now, calculate the discriminant:

D = (-\sqrt{5})^2 - 4 \times 2 \times 1

D = 5 - 8

D = -3

Since the discriminant is negative (

\displaystyle D < 0

), the quadratic equation has no real roots (the roots are imaginary/complex numbers).
Hence, **Option C** is the correct answer.

About This Chapter: Equations

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Linear, Quadratic and Cubic Equations

This chapter covers Linear, Quadratic and Cubic Equations and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

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The quadratic equation 2x2−5x+1=0\displaystyle 2x^2 - \sqrt{5}x + 1 = 02x2−5​x+1=0 has