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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The quadratic equation has degree

2

The cubic equation has degree

3

A bi-quadratic equation has degree

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.

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