Understanding the Fundamental Theorem of Algebra The Fundamental Theorem of Algebra is a cornerstone concept in mathematics that establishes a profound relationship between polynomial equations and their roots. In essence, it asserts that every non-constant polynomial equations of degree n with complex coefficients has exactly n roots in the set of complex numbers, counting multiplicities. … Read more
To simplify the expression 2n2 + 4n + 44n + 5 using the horizontal method, we’ll follow these steps: Combine Like Terms: In the expression, we can see that we have two terms with ‘n’: 4n and 44n. We can combine these terms to simplify our expression. Rewrite the Expression: After combining, we get: 2n2 … Read more
To find the solutions to the quadratic equation 2x² + 16x + 50 = 0, we can use the quadratic formula, which is given by: x = (-b ± √(b² – 4ac)) / 2a In this equation, a, b, and c are the coefficients from the standard form of a quadratic equation ax² + bx … Read more
To determine the slope of a line represented by the equation in slope-intercept form, we need to identify the coefficients in the equation, which typically has the format: y = mx + b In this equation, m represents the slope, and b is the y-intercept. For the equation y = 12x + 14: The coefficient … Read more
How to Divide 262 by 9 Using Long Division Dividing 262 by 9 might seem tricky at first, but using the long division method can make it much easier! Let’s break it down step-by-step. Step 1: Set Up the Long Division Start by writing 262 inside the long division symbol (the dividend) and 9 outside … Read more
The highest common factor (HCF) is the largest number that can divide two or more numbers without leaving a remainder. When we say that the HCF of two numbers is 1, it indicates that these two numbers are coprime, which means they have no common factors other than 1. For example, consider the numbers 8 … Read more
To determine the value of f5, we first need to clarify the relationships presented in your question regarding the functions f1 and f2. Given that f1 = 32, we can start there. If the notation fx = 1 52 fx is referring to some kind of recursive or functional relationship, it needs to be unpacked. … Read more
To simplify the expression 35 + 13 – 8 – 6, we need to follow the order of operations, which tells us to perform addition and subtraction from left to right. Let’s break it down step by step: First, we start with the addition: 35 + 13. This gives us 48. Next, we move to … Read more
To find the general solution of the higher order differential equation y”” + 2y = 0, we’ll follow a systematic approach. Step 1: Write the Characteristic Equation The first step in solving a linear homogeneous differential equation is to form the characteristic equation. For a differential equation of the form y”” + ay = 0, … Read more
To find the number that, when multiplied by both 9 and 7, results in 63, we can set up an equation. Let’s denote the unknown number as x. The equation based on the problem statement is: 9 * 7 * x = 63 First, we need to simplify the left side of the equation: 63 … Read more