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

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

Question:

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

Given:

Equation: (x + 1)2 = 2(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 algebraic identity (a + b)2 = a2 + 2ab + b2.

Solution:

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

⇒ x2 + 2(x)(1) + 12 = 2(x – 3)

⇒ x2 + 2x + 1 = 2x – 6
Move all terms to one side to get the standard form ax2 + bx + c = 0:

⇒ x2 + 2x - 2x + 1 + 6 = 0

⇒ x2 + 7 = 0
Compare this equation to the standard form ax2 + bx + c = 0:

Here, a = 1, b = 0, c = 7.
Since the coefficient of x2 (a) is 1 (which is not equal to 0), this equation is a quadratic equation.

Result:

The given equation (x + 1)2 = 2(x – 3) simplifies to x2 + 7 = 0. Since the coefficient of x2 is 1 ≠ 0, it is a quadratic equation.
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