Question

Ram has a rectangular plot whose area is 25 2 -35a+12. a) Give possible expressions for the length and breadth of rectangle. b) Can we say that the above expressions of length and breadth are factors of the  given polynomial? c) Which mathematical concept has been covered in this problem? d) What is the value of the given polynomial if a=-1 e) What is the degree of given polynomial?​

Answer 1

Answer:

Mathematics NCERT Grade 10, Chapter 4 Quadratic Equations. In the beginning, an example of a rectangular prayer hall is given and from the given situation length and breadth of a rectangular hall is obtained. This example is given to show how the quadratic equations can be used to solve real-life problems.

ax2 + bx + c = 0 is the standard form of a quadratic equation where a ≠ 0. In the first exercise, students will learn how to check whether the given equation is quadratic or not and representing the same. Various word problems are given and students need to form quadratic equation from the given word problem.

The next section is about the topic- Solution of Quadratic equation by factorisation. Roots of the equation can be found by factorising the equation into two linear factors and then equating each factor to zero. In exercise 4.2 students have to find roots of the following equation by factorisation method.

The next part is about the solution of a Quadratic equation by completing the squares. This concept is made more understandable by the illustration of figures. Problems given in the next exercise is based on the same concept.

The next method given is the use of quadratic formula. This is the most important method used to solve the quadratic equation.

In exercise 4.3 students will find several word problems that will help them to make their concept more clear.

Thus to conclude there are three methods to solve a quadratic equation:

FACTORISATION METHOD

COMPLETING SQUARES

QUADRATIC FORMULA

Once we have studied different methods of solving a quadratic equation, nature of roots is discussed. Based on the value of discriminant, a quadratic equation can have:

TWO DISTINCT REAL ROOTS: Discriminant is greater than 0.

TWO REAL EQUAL ROOTS: Discriminant is equal to 0.

NO REAL ROOTS: Discriminant is less than 0.