Exercise 2.1 Class 9 maths

#mathsclass9 #rajansir Exercise 2.1 Class 9 maths Exercise 2.1 Class 9 maths by ‪@rajansir07‬ for Online Class Call-9811757843 Class 9 Chapter 2 – Polynomials Exercise 2.1 1. Which of the following expressions are polynomials in one variable, and which are not? State reasons for your answer. (i) 4x2–3x+7 Solution: The equation 4x2–3x+7 can be written as 4x2–3x1+7x0 Since x is the only variable in the given equation and the powers of x (i.e., 2, 1 and 0) are whole numbers, we can say that the expression 4x2–3x+7 is a polynomial in one variable. (ii) y2+√2 Solution: The equation y2+√2 can be written as y2+√2y0 Since y is the only variable in the given equation and the powers of y (i.e., 2 and 0) are whole numbers, we can say that the expression y2+√2 is a polynomial in one variable. (iii) 3√t+t√2 Solution: The equation 3√t+t√2 can be written as 3t1/2+√2t Though t is the only variable in the given equation, the power of t (i.e.,1/2) is not a whole number. Hence, we can say that the expression 3√t+t√2 is not a polynomial in one variable. (iv) y+2/y Solution: The equation y+2/y can be written as y+2y-1 Though y is the only variable in the given equation, the power of y (i.e.,-1) is not a whole number. Hence, we can say that the expression y+2/y is not a polynomial in one variable. (v) x10+y3+t50 Solution: Here, in the equation x10+y3+t50 Though powers 10, 3, and 50 are whole numbers, there are 3 variables used in the expression. x10+y3+t50. Hence, it is not a polynomial in one variable. (i) x2+x Solution: The highest power of x2+x is 2 The degree is 2. Hence, x2+x is a quadratic polynomial. (ii) x–x3 Solution: The highest power of x–x3 is 3. The degree is 3. Hence, x–x3 is a cubic polynomial. (iii) y+y2+4 Solution: The highest power of y+y2+4 is 2. the degree is 2 Hence, y+y2+4is a quadratic polynomial (iv) 1+x Solution: The highest power of 1+x is 1 The degree is 1. Hence, 1+x is a linear polynomial. (v) 3t Solution: The highest power of 3t is 1. The degree is 1. Hence, 3t is a linear polynomial. (vi) r2 Solution: The highest power of r2 is 2. The degree is 2. Hence, r2 is a quadratic polynomial. (vii) 7x3 Solution: The highest power of 7x3 is 3. The degree is 3.