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# Quadratic Equations CBSE NCERT Notes Class 10 Maths PDF

Hi students, Welcome to AMBiPi (Amans Maths Blogs). In this article, you will get Quadratic Equations CBSE Notes Class 10 Maths Chapter 4 PDF. You can download this PDF and save it in your mobile device or laptop etc.

# Quadratic Equations CBSE Notes Class 10 Maths Chapter 4

The standard form of a quadratic polynomial is p(x) = ax2 + bx + c. Then, ax2 + bx + c = 0 is the general equation of quadratic equations, where a, b and c are real and a 0.

Since the degree of a quadratic equation is two, then the quadratic equation is satisfied by exactly two roots which may be real of imaginary.

### Class 10 Maths Chapter 4 Examples 1:

Check whether the equation x3 – 4x2 – x + 1 = (x – 2)3 is quadratic or not.

x3 – 4x2 – x + 1 = (x – 2)3

⇒ x3 – 4x2 – x + 1 = x3 – 8 – 6x2 + 12x

⇒ – 4x2 – x + 1 = – 8 – 6x2 + 12x

⇒ 2x2 – 13x + 9 = 0

It is of the form ax2 + bx + c = 0. So, the given equation is a quadratic equation.

## Solution of Quadratic Equations : By Factorization

A real number x = α is a root of the quadratic equation ax2 + bx + c = 0, a ≠ 0 if α satisfies the quadratic equation it means, a α2 + bα + c = 0.

### Class 10 Maths Chapter 4 Examples 2:

Find the roots of the following quadratic equations by factorization: x2 – 3x – 10 = 0.

x2 – 3x – 10 = 0

⇒ x2 – 5x + 2x – 10 = 0

⇒ x(x – 5) + 2(x – 5) = 0

⇒ (x + 2)(x – 5) = 0

⇒ x = -2 or 5

## Solution of Quadratic Equations : By Method of Completing Square

### Class 10 Maths Chapter 4 Examples 2:

Find the roots of the following quadratic equations by method of completing the square: 3x2 – 5x + 2 = 0.

Given that 3x2 – 5x + 2 = 0 The roots of the quadratic equation ax2 + bx + c = 0 are Thus, the sum of the roots is α + β = -b/a and the product of the roots is αβ = c/a.

### Class 10 Maths Chapter 4 Examples 3:

Solve the quadratic equation 2x2 + x – 528 = 0 by using quadratic formula.

Given that a = 2, b = 1 and c = -528 ## Nature of Roots of Quadratic Equations

In a quadratic equation ax2 + bx + c = 0, the value D = b2 – 4ac is known as discriminant of the quadratic equation.

The nature of the roots of the quadratic equation depends on the discriminant.

Case I: When D > 0

In this case, the roots α and β of the quadratic equation are real and unequal.

Case II: When D = 0

In this case, the roots α and β of the quadratic equation are real and equal.

Case III: When D < 0

In this case, the roots α and β of the quadratic equation are imaginary and distinct.

### Class 10 Maths Chapter 4 Examples 4:

Find the nature of the roots of the quadratic equation 2x2 – 4x + 3 = 0.

Given that a = 2, b = -4 and c = 3.

Since the discriminant b2 – 4ac = (– 4)2 – (4 × 2 × 3) = 16 – 24 = – 8 < 0

Thus, So, the given equation has no real roots.

### Class 10 Maths Chapter 4 Examples 5:

Find the values of k for each of the quadratic equation 2x2 + kx + 3 = 0, so that they have two
equal roots.

Given that a = 2, b = k and c = 3.

Since the given equation has equal roots, then

D = b2 – 4ac = 0

⇒ k2 – (4 × 2 × 3) = 0

⇒ k2 = 24

⇒ k = 2√3.

Click below to get CBSE Class 10 Maths Chapter wise Revision Notes PDF.

Chapter No Chapter name
Chapter 1 : Real Numbers CBSE Class 10 Maths Revision Notes
Chapter 2 : Polynomials CBSE Class 10 Maths Revision Notes
Chapter 3 : Pair of Linear Equations in Two Variables CBSE Class 10 Maths Revision Notes
Chapter 4 : Quadratic Equations CBSE Class 10 Maths Revision Notes
Chapter 5 : Arithmetic Progression CBSE Class 10 Maths Revision Notes
Chapter 6 : Triangles CBSE Class 10 Maths Revision Notes
Chapter 7 : Coordinate Geometry CBSE Class 10 Maths Revision Notes
Chapter 8 : Introduction to Trigonometry CBSE Class 10 Maths Revision Notes
Chapter 9 : Some Applications of Trigonometry CBSE Class 10 Maths Revision Notes
Chapter 10 : Circles CBSE Class 10 Maths Revision Notes
Chapter 11 : Constructions CBSE Class 10 Maths Revision Notes
Chapter 12 : Area Related to Circles CBSE Class 10 Maths Revision Notes
Chapter 13 : Surface Areas & Volumes CBSE Class 10 Maths Revision Notes
Chapter 14 : Statistics CBSE Class 10 Maths Revision Notes
Chapter 15 : Probability CBSE Class 10 Maths Revision Notes
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