Maths Chapter 7 Questions
Question 1: What is the quadratic formula?
The quadratic formula is a formula used to solve quadratic equations, which are equations with one variable squared. The formula is written as:
x = (-b ± √(b² - 4ac)) / 2a
- x is the variable being solved for
- a, b, and c are coefficients of the quadratic equation
- ± represents both the plus and minus signs
- √ represents the square root
Question 2: How do you factor a quadratic equation?
Factoring a quadratic equation means to write it as a product of two factors. To factor a quadratic equation, follow these steps:
- Write the quadratic equation in the form ax² + bx + c = 0
- Find two numbers that multiply to give c and add to give b
- Write the quadratic equation as (x + [first number])(x + [second number]) = 0
- Solve for x by setting each factor equal to zero
Question 3: What is the difference between a linear equation and a quadratic equation?
A linear equation is an equation with a degree of 1, meaning that the variable is not squared. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.
A quadratic equation is an equation with a degree of 2, meaning that the variable is squared. It can be written in the form y = ax² + bx + c, where a, b, and c are coefficients. Quadratic equations can have one, two, or zero real solutions, while linear equations always have exactly one solution.
Question 4: How do you solve a system of equations?
A system of equations is a set of two or more equations with two or more variables that must be solved simultaneously. To solve a system of equations, follow these steps:
- Write the equations in standard form
- Choose a variable to eliminate by either adding or subtracting the equations
- Combine the equations to eliminate the chosen variable and solve for the remaining variable
- Substitute the value found for the remaining variable back into one of the original equations to solve for the other variable