NCERT Class X Chapter 4: Quadratic Equation Example 7

NCERT Class X Chapter 4: Quadratic Equation Example 7

Question:

Find the discriminant of the quadratic equation 2x2 – 4x + 3 = 0, and hence find the nature of its roots.

Given:

The quadratic equation: 2x2 – 4x + 3 = 0

To Find:

1. The discriminant of the equation.
2. The nature of its roots.

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 (or two distinct complex roots).

Solution:

The given quadratic equation is 2x2 – 4x + 3 = 0.
Comparing it with the standard form ax2 + bx + c = 0, we have:
a = 2
b = -4
c = 3

Now, calculate the discriminant (Δ):
⇒ Δ = b2 - 4ac
⇒ Δ = (-4)2 - 4(2)(3)
⇒ Δ = 16 - 24
⇒ Δ = -8

Determine the nature of the roots based on the value of Δ:
Since Δ = -8, which is less than 0 (Δ < 0), the equation has no real roots.

Result:

The discriminant of the quadratic equation 2x2 – 4x + 3 = 0 is -8.
Since the discriminant is less than zero (Δ < 0), the quadratic equation has no real roots.
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