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

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

Question:

Check whether the following are quadratic equations: 

x(x + 1) + 8 = (x + 2) (x – 2)

Given:

Equation: x(x + 1) + 8 = (x + 2) (x – 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.

Solution:

The given equation:
x(x + 1) + 8 = (x + 2) (x – 2)
Expand the left side:
⇒ x2 + x + 8
WKT, the algebraic identity (a + b)(a - b) = a2 - b2
Expand the right side using the identity (a + b)(a - b)
⇒ x2 - 22 = x2 - 4
Substitute the expanded forms back into the equation:
⇒ x2 + x + 8 = x2 - 4
Move all terms to one side to get the standard form ax2 + bx + c = 0:
⇒ x2 - x2 + x + 8 + 4 = 0
⇒ 0x2 + x + 12 = 0
⇒ x + 12 = 0
Compare this equation to the standard form ax2 + bx + c = 0:
Here, a = 0, b = 1, c = 12.
Since the a (coefficient of x2) is 0, this equation is not a quadratic equation.

Result:

The given equation x(x + 1) + 8 = (x + 2) (x – 2) simplifies to x + 12 = 0.
Since the coefficient of x2 is 0, it is not a quadratic equation;
The given equation x(x + 1) + 8 = (x + 2) (x – 2) is a linear equation.
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