Prove that √5 is irrational Sol. Let us assume to the contrary that √5 is an irrational number. So it can be written in the form of p/q where p and q are co-prime integers and q is not equal to zero. √5= p/q squaring both sides (√5)² = (p/q)² 5= p²/q² p²= 5 q²…
Exercise 4.3 class 10 maths 1. Find the nature of the roots of the following quadratic equations. If the real roots exist ,find them. (i) 2x² – 3x + 5 =0 Here a = 2 , b = -3 , c = 5 D = b² – 4ac D = (-3)² – 4…
exercise 4.2 class 10 maths 1. Find the roots of the following quadratic equations by factorization. (i) x² – 3x – 10 = 0 (ii) 2x² + x – 6 = 0 (iii) √2 x² + 7x + 5√2 = 0 (iv) 2x² – x + 1/8 = 0 (v) 100x² – 20x + 1…
exercise 4.1 class 10 maths 1. Check whether the following are quadratic equations : 2. Represent the following situations in the form of quadratic equations: (i) The area of a rectangular plot is 528 m². The length of the plot ( in metres) is one more than twice its breadth. We need to find the…
exercise 3.3 class 10 maths 1. Solve the following pair of linear equations by the elimination method and the substitution method. Put x= 2 in (ii) 3(2) – y = 9 6 – y = 9 – y = 9 – 6 y = -3 2. Form the pair of linear equations in the following…
exercise 3.2 class 10 maths 1. Solve the following pair of linear equations by substitution method.                                5 = -2 m + 3                               2 = – 2m                              m = -1 Ans. 3. Form the pair of linear equations for the following problems and find their solution by substitution method. (i) The difference between…
exercise 3.1 class 10 maths 1. Form the pair of linear equations in the following problems, and find their solutions graphically. (i) 10 students of Class X took part in a Mathematics quiz. If number of girls is 4 more than the number of boys,find the number of boys and girls who took part in…
exercise 2.2 class 10 maths 1 Find the zeroes of the following Quadratic Polynomials and verify the relationship between the zeroes and the coefficients. (i) x²-2x-8 = x²-4x+2x-8 =x(x-4)+2(x-4) =(x+2)(x-4) for finding zeores x+2=0 , x=-2 x-4=0, x= 4 so zeroes are -2,4 Verifications : Sum of zeroes = -2+ 4 = 2= -(-2)/1 =…
exercise 2.1 class 10 maths Solutions: For finding number of zeroses of polynomials from graph, we need to check that how many times the graph cuts the x-axis, that will be the number of zeroses of that polynomial (i) in this part the graph of the polynomial do not cut x-axis , so it has…
exercise 1.2 Class 10 Maths 1. Prove that √5 is irrational. Sol. Let us assume to the contrary that √5 is an irrational number. So it can be written in the form of p/q where p and q are coprime integers and q is not equal to zero. √5= p/q squaring both sides (√5)² =…
