Quadratic Equation

is a quadratic equation in the variable x. Here a, b, c are real numbers and a ≠ 0
If α is the root of quadratic equation
Then

Quadratic Formula :

For a given quadratic equation, The roots can be given by

Exercise 4.1 (NCERT Solution) - Part - 1

1. Check whether the following are quadratic equations:

Since, the equation is in the form of So, it is a quadratic equation.

Since, the equation is in the form of So, it is a quadratic equation.

Since, the equation is not in the form of So, it is not a quadratic equation.

Since, the equation is in the form of So, it is a quadratic equation.

Since, the equation is in the form of So, it is a quadratic equation.

Since, the equation is not in the form of So, it is not a quadratic equation.

Since, the equation is not in the form of So, it is not a quadratic equation.

Since, the equation is in the form of So, it is a quadratic equation. 

Exercise 4.1 (NCERT Solution) - Part - 2

Question: 2 – Represent the following situation in the form of quadratic equation:
(i) The area of a rectangular plot is 528 m2. The length of the plot (in meters) is one more than twice its breadth. We need to find the length and breadth of the plot.

Solution:

Since, the equation is in the form of So, it is a quadratic equation.

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

Solution:

Since, the equation is in the form of So, it is a quadratic equation.

(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 the Rohan’s age.

Solution:

Since, the equation is in the form of So, it is a quadratic equation.

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

Solution:

Since, the equation is in the form of So, it is a quadratic equation.