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

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

Question:

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

Given:

Equation: (x – 2)(x + 1) = (x – 1)(x + 3)

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, the product of two binomials (a + b)(c + d) = ac + ad + bc + bd.

Solution:

Start with the given equation:

(x – 2)(x + 1) = (x – 1)(x + 3)
Expand the left side:

⇒ x(x) + x(1) - 2(x) - 2(1) = x2 + x - 2x - 2 = x2 - x - 2
Expand the right side:

⇒ x(x) + x(3) - 1(x) - 1(3) = x2 + 3x - x - 3 = x2 + 2x - 3
Substitute the expanded forms back into the equation:

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

⇒ x2 - x2 - x - 2x - 2 + 3 = 0

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

Here, a = 0, b = -3, and c = 1.
Since the coefficient of x2 (a) is 0, this equation is not a quadratic equation; it is a linear equation.

Result:

The given equation (x – 2)(x + 1) = (x – 1)(x + 3) simplifies to -3x + 1 = 0. Since the coefficient of x2 is 0, it is not a quadratic equation.
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