NCERT Class X Chapter 4: Quadratic Equation Example 2 (i)

NCERT Class X Chapter 4: Quadratic Equation Example 2 (i)

Question:

Check whether the following are quadratic equations: 

(x – 2)2 + 1 = 2x – 3

Given:
Equation: (x – 2)2 + 1 = 2x – 3
To Find:
Whether the given equation is a quadratic equation.
Formula:
A quadratic equation is of the form ax2 + bx + c = 0, where a ≠ 0.
Solution:

The given equation: (x – 2)2 + 1 = 2x – 3
Expand (x – 2)2 using (a - b)2 formula (a - b)2 = a2 - 2ab + b2

⇒ x2 - 2(x)(2) + 22 + 1 = 2x – 3

⇒ x2 - 4x + 4 + 1 = 2x – 3
Simplify the left side:

⇒ x2 - 4x + 5 = 2x – 3
Move all terms to one side to get the standard form ax2 + bx + c = 0:

⇒ x2 - 4x - 2x + 5 + 3 = 0 ⇒  x2 - 6x + 8 = 0
Compare this equation to the standard form ax2 + bx + c = 0:

Here, a = 1, b = -6, c = 8.

Since a = 1 (which is not equal to 0), the equation is a quadratic equation.
Result:
The given equation (x – 2)2 + 1 = 2x – 3 simplifies to x2 - 6x + 8 = 0, which is in the form ax2 + bx + c = 0 with a = 1 ≠ 0.

Therefore, it is a quadratic equation.
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