Originally posted by denian
i do not type wrongly
if x=2 is a root of ax^2 - bx -x = 0, state the relationship connecting a,b, c
Originally posted by denian
the answer for the first part of the question is
4a - 2b - c = 0.
show that x=2 is also a root of
bx^2 + cx - 8a = 0.
A function is a mathematical relationship between an input and an output. It takes in a value or set of values as input and produces a corresponding output. A function can be represented in various ways, such as an equation, table, or graph.
To determine if an equation is a function, you can use the vertical line test. This involves drawing a vertical line on a graph and seeing if it crosses the graph at more than one point. If it does, then the equation is not a function. Alternatively, you can also check if each input has a unique output in a table of values or by solving for y in the equation.
A quadratic equation is an equation in the form of ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. It represents a parabola on a graph and has a degree of 2. Quadratic equations can have two solutions, one solution, or no real solutions depending on the value of the discriminant, b^2 - 4ac.
To solve a quadratic equation, you can use the quadratic formula, x = (-b ± √(b^2 - 4ac)) / 2a, where a, b, and c are the coefficients in the equation. You can also factor the equation or complete the square to find the solutions. Additionally, you can use a graphing calculator to find the x-intercepts of the parabola.
Quadratic equations have many real-world applications, such as finding the maximum or minimum value of a quantity, predicting the path of a projectile, and determining the optimal shape for certain structures. They are also used in fields like engineering, physics, and economics to model and solve various problems.