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Quadratic equations are the NCERT chapter which deals with algebraic equations of degree 2. The NCERT Class 10 Maths chapter 4 notes covers a brief outline of the chapter quadratic equations. The main topics covered quadratic equations Class 10 notes, gives you properties and roots of quadratic equations. Class 10 Maths chapter 4 notes also cover the basic equations in the chapter. Quadratic equations Class 10 notes pdf download contains all of these topics.
Also, students can refer,
Quadratic Polynomial
A polynomial with degree 2, is a quadratic polynomial. It is in the form of
f(x) = ax^{2} + bx + c, where a ≠ 0
Quadratic Equation
An algebraic expression of the second degree is called a quadratic equation.
The standard form of a Quadratic Equation
ax^{2}+bx+c=0
where a, b and c are the real numbers and a≠0
Let x = α and α is a real number. If α satisfies the quadratic equation ax^{2}+ bx + c = 0 such that aα^{2} + bα + c = 0, then α is the root of the Quadratic Equation.
As quadratic polynomials have degree two, therefore quadratic equations can have two roots. Thus, the zeros of a quadratic polynomial f(x) =ax^{2}+bx+c is same as the roots of the quadratic equation ax^{2}+ bx + c= 0.
Three methods to solve the Quadratic Equations-
In this method, divide the equation into two linear factors and equate each factor to zero to find the roots of the equation.
Step 1: Quadratic Equation in the form of ax^{2} + bx + c = 0.
Step 3: By factorization, we write ax^{2 }+ bx + c = 0 as (x + p) (x + q) = 0
For example-
x^{2}-2x-15=0
(x+3)(x-5)=0
x+3=0 or x-5=0
x=-3 or x=5
x={-3,5}
The above values of x are the two roots of the given quadratic equation.
In this method, convert the equation in the square form (x + a)^{2} - b^{2}= 0 to find the roots.
Step1: Quadratic Equation in the standard form ax^{2 }+ bx + c = 0.
Step 2: Divide both the sides by a:
Step 3: Transfer the constant to RHS then add the square of the half of the coefficient of x i.e. (b/2a)^{2 }on both the sides
Step 4: Write LHS as a perfect square and simplify RHS.
Step 5: Square root on both sides.
Step 6: Constant terms are shifted to the RHS and calculate the value of x as there is no variable at the RHS.
In this method, find the roots by using the quadratic formula. The quadratic formula is
where a, b and c are the real numbers and b^{2 }– 4ac is known as a discriminant.
The nature of the roots of the equation depends upon the value of D, which is called the discriminant.
Value of discriminant | Number of roots |
D>0 | Two distinct real roots |
D=0 | Two equal and real roots |
D<0 | No real roots |
Quadratic Equations Class 10 notes will help to understand the formulas, statements, rules in detail.
This NCERT Class 10 Maths chapter 4 notes also contains previous year’s questions and NCERT TextBook pdf. It also contains FAQs or frequently asked questions along with topic-wise explanations.
In offline mode, Class 10 Maths chapter notes pdf download can be used to prepare.
The process by which the bracket of a quadratic equation is reduced is called factorization.
Students can expect 4 to 8 marks questions from the notes for Class 10 Math’s chapter 4.
In the notes for Class 10 Math’s chapter 4, four methods are discussed to find the roots of a quadratic equation.
It is evident that this chapter gives a better understanding of quadratic polynomials and helps us understand quadratic equations in a more wholesome way. Students can use Class 10 Math’s chapter 4 notes pdf download for revision
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