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

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

Question:

Check whether the following are quadratic equations :
(x – 3)(2x +1) = x(x + 5)

Given:

Equation: (x – 3)(2x +1) = x(x + 5)

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 – 3)(2x +1) = x(x + 5)
Expand the left side:

⇒ x(2x) + x(1) - 3(2x) - 3(1) = 2x2 + x - 6x - 3
= 2x2 - 5x - 3
Expand the right side:

⇒ x(x) + x(5) = x2 + 5x
Substitute the expanded forms back into the equation:

⇒ 2x2 - 5x - 3 = x2 + 5x
Move all terms to one side to get the standard form ax2 + bx + c = 0:

⇒ 2x2 - x2 - 5x - 5x - 3 = 0

⇒ x2 - 10x - 3 = 0
Compare this equation to the standard form ax2 + bx + c = 0:

Here, a = 1, b = -10, c = -3.
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 – 3)(2x +1) = x(x + 5) simplifies to x2 - 10x - 3 = 0. Since the coefficient of x2 is 1 ≠ 0, it is a quadratic equation.
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