*Watch the first video session on “Quadratic Equations” for Class X*^{th} – concepts and solved questions.

^{th}– concepts and solved questions.

**Quadratic Equations – Class X – Part 1 | Exercise 4.1 Solved**

When we equate quadratic polynomial of the form ax^2 + bx + c, to zero, we get a quadratic equation.

A quadratic equation in the variable x is an equation of the form ax^2 + bx + c = 0, where a, b, c are real numbers, a ≠ 0. Any equation of the form p(x) = 0, where p(x) is a polynomial of degree 2, is a quadratic equation. ax^2 + bx + c = 0, a ≠ 0 is called the standard form of a quadratic equation.

**EXERCISE 4.1**

1. Check whether the following are quadratic equations :

(i) (x + 1)^{2} = 2(x – 3) (ii) x^{2} – 2x = (–2) (3 – x)

(iii) (x – 2)(x + 1) = (x – 1)(x + 3) (iv) (x – 3)(2x +1) = x(x + 5)

(v) (2x – 1)(x – 3) = (x + 5)(x – 1) (vi) x^{2} + 3x + 1 = (x – 2)^{2}

(vii) (x + 2)^{3} = 2x (x^{2} – 1) (viii) x^{3} – 4x^{2} – x + 1 = (x – 2)^{3}

2. Represent the following situations in the form of quadratic equations :

(i) The area of a rectangular plot is 528 m^{2}. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

(ii) The product of two consecutive positive integers is 306. We need to find the integers.

(iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

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