devyy To find the zeros of the function f(x) = x² + 8x + 4, we need to solve the equation f(x) = 0. This means we will set the quadratic equation to zero: x² + 8x + 4 = 0 To solve this quadratic equation, we can use the quadratic formula: x = (-b ± … Read more
Understanding the Behavior of the Polynomial The function in question is a polynomial of degree five, which means it can have up to five real roots in total. One important aspect to consider here is how many of these roots can be negative real roots. Applying Descartes’ Rule of Signs To determine the possible number … Read more
When we talk about the factors of 1000, we are discussing the numbers that can be multiplied together to yield 1000 as a product. One straightforward way to identify these factors is to start with the number itself and work your way down to 1. The prime factorization of 1000 yields: 1000 = 10 x … Read more
To determine the value of fg(x) when x equals 1, we need to evaluate the composite function fg(x). This means we will first find g(1) and then use that result to find f(g(1)). Step 1: Calculate g(1) The function g(x) is defined as: g(x) = x + 3 Substituting x = 1 into g(x): g(1) … Read more
To find the value of f(3) for the function f(x) = 2×3 + 7, you need to substitute the value of x with 3 in the given function. Here’s the step-by-step process: Start with the function: f(x) = 2×3 + 7 Substitute 3 into the function for x: f(3) = 2(3)3 + 7 Calculate 33: … Read more
To find the sine given that the cotangent of an angle is 2 and the cosine is 0, we can use our understanding of trigonometric identities and properties. Let’s denote the angle as θ. 1. **Understanding Cotangent and Cosine:** The cotangent of an angle is defined as: cot(θ) = cos(θ) / sin(θ) Given that cot(θ) … Read more
Finding the HCF of 399 and 437 Using the Division Method To calculate the Highest Common Factor (HCF) of 399 and 437 using the division method, follow these systematic steps: Step 1: Initial Division Start by dividing the larger number (437) by the smaller number (399). 437 ÷ 399 = 1 with a remainder of … Read more
To verify the identity cos(4x) cos(2x) = 2 sin²(2x) sin²(x), we can start by simplifying both sides. Step 1: Simplifying the Left Side Using the double angle formulas, we know: cos(4x) = 2cos²(2x) – 1 cos(2x) = 2cos²(x) – 1 So we can express the left side as: Left Side: cos(4x) cos(2x) = (2cos²(2x) – … Read more
To calculate the slope of a line passing through two points, we use the formula: Slope (m) = (y2 – y1) / (x2 – x1) In this case, we have the points (1, 4) and (1, 3). Here, let’s identify the coordinates: First point (x1, y1): (1, 4) Second point (x2, y2): (1, 3) Substituting … Read more
To simplify the expression x² + 15x + 365x + 60, we start by combining like terms. In this expression, the like terms are the linear terms involving x. Let’s break it down: The quadratic term is: x² The linear terms are: 15x and 365x The constant term is: 60 Now, add the coefficients of … Read more