Page 1 Mathematics (www.tiwariacademy.net) (Class X) www.tiwariacademy.com A Free web support in education 1 Question 1: Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. Answer 1: The value of is zero when x - 4 = 0 or x + 2 = 0, i.e., when x = 4 or x = -2 The value of 4s 2 - 4s + 1 is zero when 2s - 1 = 0, i.e., Therefore, the zeroes of 4s 2 - 4s + 1 are ½ and ½ . Sum of zeroes = The value of 6x 2 - 3 - 7x is zero when 3x + 1 = 0 or 2x - 3 = 0, i.e., Therefore, the zeroes of are 4 and -2. Sum of zeroes = Product of zeroes Product of zeroes Page 2 Mathematics (www.tiwariacademy.net) (Class X) www.tiwariacademy.com A Free web support in education 1 Question 1: Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. Answer 1: The value of is zero when x - 4 = 0 or x + 2 = 0, i.e., when x = 4 or x = -2 The value of 4s 2 - 4s + 1 is zero when 2s - 1 = 0, i.e., Therefore, the zeroes of 4s 2 - 4s + 1 are ½ and ½ . Sum of zeroes = The value of 6x 2 - 3 - 7x is zero when 3x + 1 = 0 or 2x - 3 = 0, i.e., Therefore, the zeroes of are 4 and -2. Sum of zeroes = Product of zeroes Product of zeroes Mathematics (www.tiwariacademy.net) (Class X) www.tiwariacademy.com A Free web support in education 2 The value of 4u 2 + 8u is zero when 4u = 0 or u + 2 = 0, i.e., u = 0 or u = -2 Therefore, the zeroes of 4u 2 + 8u are 0 and -2. The value of t 2 - 15 is zero when , i.e., when or Therefore, the zeroes of 6 x 2 - 3 - 7 x are . Sum of zeroes = Product of zeroes = Sum of zeroes = Product of zeroes = or Page 3 Mathematics (www.tiwariacademy.net) (Class X) www.tiwariacademy.com A Free web support in education 1 Question 1: Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. Answer 1: The value of is zero when x - 4 = 0 or x + 2 = 0, i.e., when x = 4 or x = -2 The value of 4s 2 - 4s + 1 is zero when 2s - 1 = 0, i.e., Therefore, the zeroes of 4s 2 - 4s + 1 are ½ and ½ . Sum of zeroes = The value of 6x 2 - 3 - 7x is zero when 3x + 1 = 0 or 2x - 3 = 0, i.e., Therefore, the zeroes of are 4 and -2. Sum of zeroes = Product of zeroes Product of zeroes Mathematics (www.tiwariacademy.net) (Class X) www.tiwariacademy.com A Free web support in education 2 The value of 4u 2 + 8u is zero when 4u = 0 or u + 2 = 0, i.e., u = 0 or u = -2 Therefore, the zeroes of 4u 2 + 8u are 0 and -2. The value of t 2 - 15 is zero when , i.e., when or Therefore, the zeroes of 6 x 2 - 3 - 7 x are . Sum of zeroes = Product of zeroes = Sum of zeroes = Product of zeroes = or Mathematics (www.tiwariacademy.net) (Class X) www.tiwariacademy.com A Free web support in education 3 The value of 3x 2 - x - 4 is zero when 3x - 4 = 0 or x + 1 = 0, i.e., when or x = -1 Therefore, the zeroes of 3x 2 - x - 4 are 4/3 and -1. Sum of zeroes = Product of zeroes Question 2: Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. Answer 2: Therefore, the zeroes of t 2 - 15 are and . Sum of zeroes = Product of zeroes = Page 4 Mathematics (www.tiwariacademy.net) (Class X) www.tiwariacademy.com A Free web support in education 1 Question 1: Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. Answer 1: The value of is zero when x - 4 = 0 or x + 2 = 0, i.e., when x = 4 or x = -2 The value of 4s 2 - 4s + 1 is zero when 2s - 1 = 0, i.e., Therefore, the zeroes of 4s 2 - 4s + 1 are ½ and ½ . Sum of zeroes = The value of 6x 2 - 3 - 7x is zero when 3x + 1 = 0 or 2x - 3 = 0, i.e., Therefore, the zeroes of are 4 and -2. Sum of zeroes = Product of zeroes Product of zeroes Mathematics (www.tiwariacademy.net) (Class X) www.tiwariacademy.com A Free web support in education 2 The value of 4u 2 + 8u is zero when 4u = 0 or u + 2 = 0, i.e., u = 0 or u = -2 Therefore, the zeroes of 4u 2 + 8u are 0 and -2. The value of t 2 - 15 is zero when , i.e., when or Therefore, the zeroes of 6 x 2 - 3 - 7 x are . Sum of zeroes = Product of zeroes = Sum of zeroes = Product of zeroes = or Mathematics (www.tiwariacademy.net) (Class X) www.tiwariacademy.com A Free web support in education 3 The value of 3x 2 - x - 4 is zero when 3x - 4 = 0 or x + 1 = 0, i.e., when or x = -1 Therefore, the zeroes of 3x 2 - x - 4 are 4/3 and -1. Sum of zeroes = Product of zeroes Question 2: Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. Answer 2: Therefore, the zeroes of t 2 - 15 are and . Sum of zeroes = Product of zeroes = Mathematics (www.tiwariacademy.net) (Class X) www.tiwariacademy.com A Free web support in education 4 Let the polynomial be ax 2 + bx + c and its zeroes be ?? and ?? . Therefore, the quadratic polynomial is 4x 2 - x - 4. Let the polynomial be ax 2 + bx + c and its zeroes be ?? and ?? . Therefore, the quadratic polynomial is 3x 2 - x + 1. Let the polynomial be ax 2 + bx + c and its zeroes be ?? and ?? . Therefore, the quadratic polynomial is . Let the polynomial be ax 2 + bx + c and its zeroes be ?? and ?? . Page 5 Mathematics (www.tiwariacademy.net) (Class X) www.tiwariacademy.com A Free web support in education 1 Question 1: Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. Answer 1: The value of is zero when x - 4 = 0 or x + 2 = 0, i.e., when x = 4 or x = -2 The value of 4s 2 - 4s + 1 is zero when 2s - 1 = 0, i.e., Therefore, the zeroes of 4s 2 - 4s + 1 are ½ and ½ . Sum of zeroes = The value of 6x 2 - 3 - 7x is zero when 3x + 1 = 0 or 2x - 3 = 0, i.e., Therefore, the zeroes of are 4 and -2. Sum of zeroes = Product of zeroes Product of zeroes Mathematics (www.tiwariacademy.net) (Class X) www.tiwariacademy.com A Free web support in education 2 The value of 4u 2 + 8u is zero when 4u = 0 or u + 2 = 0, i.e., u = 0 or u = -2 Therefore, the zeroes of 4u 2 + 8u are 0 and -2. The value of t 2 - 15 is zero when , i.e., when or Therefore, the zeroes of 6 x 2 - 3 - 7 x are . Sum of zeroes = Product of zeroes = Sum of zeroes = Product of zeroes = or Mathematics (www.tiwariacademy.net) (Class X) www.tiwariacademy.com A Free web support in education 3 The value of 3x 2 - x - 4 is zero when 3x - 4 = 0 or x + 1 = 0, i.e., when or x = -1 Therefore, the zeroes of 3x 2 - x - 4 are 4/3 and -1. Sum of zeroes = Product of zeroes Question 2: Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. Answer 2: Therefore, the zeroes of t 2 - 15 are and . Sum of zeroes = Product of zeroes = Mathematics (www.tiwariacademy.net) (Class X) www.tiwariacademy.com A Free web support in education 4 Let the polynomial be ax 2 + bx + c and its zeroes be ?? and ?? . Therefore, the quadratic polynomial is 4x 2 - x - 4. Let the polynomial be ax 2 + bx + c and its zeroes be ?? and ?? . Therefore, the quadratic polynomial is 3x 2 - x + 1. Let the polynomial be ax 2 + bx + c and its zeroes be ?? and ?? . Therefore, the quadratic polynomial is . Let the polynomial be ax 2 + bx + c and its zeroes be ?? and ?? . Mathematics (www.tiwariacademy.net) (Class X) www.tiwariacademy.com A Free web support in education 5 Therefore, the quadratic polynomial is . Let the polynomial be ax 2 + bx + c and its zeroes be ?? and ?? . Therefore, the quadratic polynomial is . Let the polynomial be ax 2 + bx + c and its zeroes be ?? and ?? . Therefore, the quadratic polynomial is .Read More

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