Quadratic formula / Shreedharacharya sutra: x=-b±√b²-4ac/2a For Finding Nature of roots: First we find Discriminant (D) : b²- 4ac There are three different cases Case I : b²-4ac<0 Nature of Roots : Imaginary Roots/ No Real roots Case II : b² – 4ac = 0 Nature of Roots : Real and two different roots Case III …
Q1. Find the roots of the following quadratic equations by factorization Method: (I) x² -3x-10 =0 by factorization method: ⇒ x² – 3x – 10 = 0 ⇒ x² – ( 5 – 2 )x – 10 = 0 ⇒ x² – 5x + 2x – 10 = 0 ⇒ x( x – 5 ) + …
Q.1. Check whether the following are quadratic equations ÷ (i) (x + 1)2 = 2 (x – 3) Solution: (x + 1)2 = 2 (x – 3) [By Applying ( a + b )² = a²+2ab+b2] ⇒ x²+2x+1= 2x – 6 ⇒ x²+2x+1 – 2x + 6 = 0 ⇒ x² + 7 = 0 …
Important formula for this Exercise: Sum of n terms of AP= Sn (i) Sn = n/2[2a+(n-1)d] (ii) Sn = n/2[a + an ] (iii) Sn = n/2[a + l ] (iv) Sum of first n positive integers = Sn = n(n+1)/2 Q.1 Find the sum of the Following APs; (i) 2, 7,12,…………to 10 terms a = first term = 2 …
Q1 Fill in the blanks in the following table, given that a is the first term d, the common difference and an the nth term of the AP: (i) a = 7 d = 3 n = 8 an = ? Solution: nth term of AP an = a + (n-1)d a8 = 7 + …
Basic Concepts Sequence: Some numbers arranged in a definite order, according to a definite rule, are said to form a sequence. eg. (i) 1,2,3,…………. (ii) 100, 60, 30, …………… (iii) -1.0, -1.5, -2.0, -2.5, ………. Arithmetic Progressions(AP): An arithmetic progression is a list of numbers on which each term is obtained by adding a fixed …
Q1. Find the distance between the Following pairs of points: (i) (2,3),(4,1) Solution: Let By Distance Formula A B = √(x2 – x1)² + (y2 – y1)² ⇒ A B = √(4 – 2)² + (1 – 3)² ⇒ A B = √(2)² + (-2)² ⇒ A B = √4 + 4 ⇒ A B …
In mathematics indices or index is the value that is raised to the power of any variable or constant like x raised to power 2 i.e. x2. Where x is a variable and 2 is called the power or exponent of that variable. Let’s see an example: axm Here a = coefficient x = base …
Mathematics वन ऑफ द मोस्ट पॉपुलर सब्जेक्ट्स में से एक है। और अगर आपको एक अच्छा टीचर और प्रॉपर गाइडेंस मिल जाये तो आप इसे एक सब्जेक्ट की तरह नहीं, एन्जॉय करते हुए पढ़ेंगे। जैसा की हम जानते है की, हमने मैथमेटिक्स के चलते इम्पॉसिबल चीजों को हल लिया है। जैसे की चाँद तक पहुँचना, …
