NCERT Class X Chapter 4: Quadratic Equation Exercise 4.3 Question 1 (i)

NCERT Class X Chapter 4: Quadratic Equation Exercise 4.3 1 (i)

Question:

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them : 2x2 – 3x + 5 = 0.

Given:

The quadratic equation: 2x2 – 3x + 5 = 0

To Find:

The nature of the roots. If real roots exist, find them.

Formula:

WKT, for a quadratic equation of the form ax2 + bx + c = 0, the discriminant (Δ) is given by:

Δ = b2 - 4ac



WKT, the nature of roots is determined by the value of the discriminant (Δ):

• If Δ > 0, there are two distinct real roots.

• If Δ = 0, there are two equal real roots.

• If Δ < 0, there are no real roots.


WKT, if the roots are real, they can be found using the quadratic formula:

x = -b ± √Δ 2a

Solution:

The given quadratic equation is 2x2 – 3x + 5 = 0.
Comparing it with the standard form ax2 + bx + c = 0, we have:

a = 2

b = -3

c = 5
Calculate the discriminant (Δ):

⇒ Δ = b2 - 4ac

⇒ Δ = (-3)2 - 4(2)(5)

⇒ Δ = 9 - 40

⇒ Δ = -31
Determine the nature of the roots:

Since Δ = -31, which is less than 0 (Δ < 0), the equation has no real roots.

Result:

The discriminant of the equation 2x2 – 3x + 5 = 0 is -31.

Since the discriminant is less than zero (Δ < 0), there are no real roots.
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