# NCERT CBSE Class 10th Mathematics Chapter 4: Quadratic Equations

Safalta Expert Published by: Sylvester Updated Wed, 22 Jun 2022 06:42 PM IST

## Highlights

NCERT CBSE Class 10th Mathematics Chapter 4: Quadratic Equations

The fourth chapter of CBSE Class 10th Mathematics is ‘Quadratic Equations’.
Students will come to know that a polynomial of the form ax2+bx+c, where a, b and c are real numbers and a≠0 is called a quadratic polynomial.
When we equate a quadratic polynomial to a constant, we get a quadratic equation.
Any equation of the form p(x)=c, where p(x) is a polynomial of degree 2 and c is a constant, is a quadratic equation.
The standard form of a quadratic equation is ax2+bx+c=0, where a,b and c are real numbers and a≠0.
‘a’ is the coefficient of x2. It is called the quadratic coefficient. ‘b’ is the coefficient of x. It is called the linear coefficient. ‘c’ is the constant term.

### Some important topics to study in this chapter are as follows:

• Factorisation method
• Completing the square method
• Nature of Roots

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4

## A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.

Let the number be x

Then according to question,

x + 12 = 160/x

x2 + 12x – 160 = 0

x2 + 20x – 8x – 160 = 0

(x + 20) (x – 8) = 0

x = -20, 8

Since the number is natural, so we consider only positive value.

## Rohini had scored 10 more marks in her mathematics test out of 30 marks, 9 times these marks would have been the square of her actual marks. How many marks did she get in the test?

Let her actual marks be x

Therefore,

9 (x + 10) = x2

⇒x2 – 9x – 90 = 0

⇒x2 – 15x + 6x – 90 = 0

⇒x(x – 15) + 6 (x – 15) = 0

⇒(x + 6) (x – 15) = 0

Therefore  x = – 6 or x =15

Since x is the marks obtained, x ≠ – 6. Therefore, x = 15.