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 …
Theorem 6.1 Thale’s Theorem/ Basic Proportionality Theorem (BPT) Statement: ” If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points. The other two sides are divided in the same ratio.” OR Prove that in a triangle a line parallel to one side divides remaining …
State and Prove Basic Proportionality (BPT) Theorem Class 10 Read More »
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 …
Q.1 Find the coordinates of the point which divides the join of (-1,7) and (4,-3) in the ratio 2:3. Solution: Let A(-1,7) and B(4, -3) and Ratio m1 : m2 = 2 : 3 fig By Section Formula Coordinate of P(x, y) x = (m1x2 + m2x1)/m1+m2 ; y = (m1y2 + m2y1)/m1+m2 ⇒ x …
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 …
Q1.Find the roots of the Following quadratic equations, if they exist, by the method of quadratic formula. Quadratic Formula/Shreedharacharya Sutra:- X =[-b ± √(b² – 4ac)]/2a Nature of Roots: Discriminant(D)= b² – 4ac 1. b²- 4ac < 0 Nature of Roots : Imaginary/No real root 2. b² – 4ac = 0 Nature of Roots: Real …
