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

Solution:

Given, the quadratic equation is 2x² - √5x + 1 = 0

We have to find the nature of the roots of the equation.

Discriminant = b² - 4ac

Here, a = 2, b = -√5 and c = 1

b² = (-√5)² = 5

4ac = 4(2)(1) = 8

b² - 4ac = 5 - 8 = -3

b² - 4ac < 0

A quadratic equation ax² + bx + c = 0 has no real roots when the discriminant of the equation is less than zero.

Therefore, the equation has no real roots.

✦ Try This: The quadratic equation x² - 5x + 10 = 0 has

1. two distinct real roots
2. two equal real roots
3. no real roots
4. more than 2 real roots

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4

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NCERT Exemplar Class 10 Maths Exercise 4.1 Problem 8

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

Summary:

The quadratic equation 2x² - √5x + 1 = 0 has no real root

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