NCERT Class X Chapter 4: Quadratic Equation Exercise 4.1 Question 1 (vi)

NCERT Class X Chapter 4: Quadratic Equation Exercise 4.1 1 (vi)

Question:

Check whether the following are quadratic equations :
x2+ 3x + 1 = (x – 2)2

Given:

Equation: x2 + 3x + 1 = (x – 2)2

To Find:

Whether the given equation is a quadratic equation.

Formula:

WKT,
A quadratic equation is of the form ax2 + bx + c = 0, where a ≠ 0
WKT,
(a - b)2 = a2 - 2ab + b2

Solution:

Start with the given equation:

x2 + 3x + 1 = (x – 2)2
Expand the right side using (a - b)2 = a2 - 2ab + b2:

⇒ x2 - 2(x)(2) + 22 = x2 - 4x + 4
Substitute the expanded form back into the equation:

⇒ x2 + 3x + 1 = x2 - 4x + 4
Move all terms to one side to get the standard form ax2 + bx + c = 0:

⇒ x2 - x2 + 3x + 4x + 1 - 4 = 0

⇒ 7x - 3 = 0
Compare this equation to the standard form ax2 + bx + c = 0:

Here, a = 0, b = 7, c = -3.
Since the coefficient of x2 (a) is 0, this equation is not a quadratic equation; it is a linear equation.

Result:

The given equation x2 + 3x + 1 = (x – 2)2 simplifies to 7x - 3 = 0.

Since the coefficient of x2 is 0, it is not a quadratic equation.
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