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

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

Question:

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

Given:

Equation: x2 – 2x = (–2) (3 – x)

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: 

Start with the given equation:

x2 – 2x = (–2) (3 – x)
Expand the right side:

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

⇒ x2 - 2x - 2x + 6 = 0

⇒ x2 - 4x + 6 = 0
Compare this equation to the standard form ax2 + bx + c = 0:

Here, a = 1, b = -4, and c = 6.
Since the coefficient of x2 (a) is 1 (which is not equal to 0), this equation is a quadratic equation.

Result:

The given equation x2 – 2x = (–2) (3 – x) simplifies to x2 - 4x + 6 = 0.

Since the coefficient of x2 is 1 ≠ 0, it is a quadratic equation.
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