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

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

Question:

Check whether the following are quadratic equations: 

x (2x + 3) = x2 + 1

Given:
Equation: x (2x + 3) = x2 + 1
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 (2x + 3) = x2 + 1
Expand the left side:

⇒ 2x2 + 3x
Substitute the expanded form back into the equation:
⇒ 2x2 + 3x = x2 + 1
Move all terms to one side to get the standard form ax2 + bx + c = 0:

⇒ 2x2 - x2 + 3x - 1 = 0

⇒ x2 + 3x - 1 = 0
Compare this equation to the standard form ax2 + bx + c = 0:

Here, a = 1, b = 3, and c = -1.
Since the a (coefficient of x2) is 1 (which is not equal to 0), this equation is a quadratic equation.
Result:

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

x2 + 3x - 1 = 0 is in the form ax2 + bx + c = 0 with a = 1 ≠ 0.

Therefore, it is a quadratic equation.
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