NCERT 10th Maths All Formula

Real Numbers

1.      Euclid’s division algorithm

                a = bq + r    where r is Reminder which is 0 ≤ r < d

                                            q is Quottient

                                            a and b are dividend and divisor; b ≠ 0

2.      Finding HCF using Euclid’s division algorithm

                

Step 1 : Apply Euclid’s division lemma, to a & b such that a > b.and find q and r such that a = bq + r, 0 ≤ r < d. 

Step 2 : If r = 0, b is the HCF of a and b.

Step 3 : If r ≠ 0, apply the division lemma to b & r. 

Step 4 : Repeat the process until the remainder r = 0. The divisor at this stage will be the required HCF.

Consider a quadratic equation:

ax2 + bx+ c = 0 with a ≠ 0

The roots of the following quadratic equation are given by:

x=−b+b2−4ac√2a  and  x=−b−b2−4ac√2a

(or)      x=−b±b2−4ac√2a

This is known as quadratic formulae for finding roots of quadratic equation.

Nature of roots:

The term (b2 – 4ac) is known as discriminant and it determines the nature of roots of the quadratic equation.

If b2 – 4ac > 0, then the equation will have two distant real roots.

If b2 – 4ac = 0, then the equation will have two equal real roots.

If b2 – 4ac < 0, then the equation will have unreal roots.