Identify the given quadratic polynomial and its zeroes.

Fresh day BILIJITIN, let's solve. Q.1.i. Step 1: Identify the given quadratic polynomial and its zeroes. The quadratic polynomial is x^2 - 3x + k. The zeroes are = 2 and = -5. Step 2: Use the relationship between the product of zeroes and the coefficients of a quadratic polynomial. For a quadratic polynomial ax^2 + bx + c, the product of the zeroes is given by (c)/(a). In x^2 - 3x + k, we have a=1, b=-3, and c=k. The product of the given zeroes is 2 × (-5) = -10. Equating this to (c)/(a): (k)/(1) = -10 k = -10 The correct alternative is (A). The final answer is (A) -10. Q.1.ii. Step 1: Recall the standard trigonometric value for 30^. The value of 30^ is a fundamental trigonometric ratio. 30^ = (1)/(2) The correct alternative is (B). The final answer is (B) (1)/(2). Q.1.iii. Step 1: Identify the given points. The two points are (x_1, y_1) = (-2, 3) and (x_2, y_2) = (4, -1). Step 2: Use the distance formula. The distance D between two points (x_1, y_1) and (x_2, y_2) is given by the formula: D = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2) Step 3: Substitute the coordinates and calculate the distance. D = sqrt((4 - (-2))^2 + (-1 - 3)^2) D = sqrt((4 + 2)^2 + (-4)^2) D = sqrt((6)^2 + (-4)^2) D = sqrt(36 + 16) D = sqrt(52) The correct alternative is (B). The final answer is (B) sqrt(52). Q.1.iv. Step 1: Identify the first five natural numbers. Natural numbers are positive integers starting from 1. The first five natural numbers are 1, 2, 3, 4, 5. Step 2: Calculate the sum of these numbers. Sum = 1 + 2 + 3 + 4 + 5 = 15. Step 3: Calculate the mean. The mean is the sum of the numbers divided by the count of the numbers. Count of numbers = 5. Mean = SumCount = (15)/(5) = 3 The correct alternative is (C). The final answer is (C) 3. Send me the next one 📸