Secondary Math 2 Module 3 Answers (2024)

FAQs

What number set to which the roots of each quadratic function belong? ›

The roots belong to the set of complex numbers, and will be called "complex roots" (or "imaginary roots"). These complex roots will be expressed in the form a ± bi. A quadratic equation is of the form ax² + bx + c = 0 where a, b and c are real number values with a not equal to zero.

A quadratic equation with real or complex coefficients has two solutions, called roots. These two solutions may or may not be distinct, and they may or may not be real.

Quadratic equations' roots are the values of the variables that satisfy the equation. They're also known as the quadratic equation's “solutions” or “zeros.” Because they satisfy the equation, the roots of the quadratic equation x² – 7x + 10 = 0 are x = 2 and x = 5. i.e., when x = 2, 22 – 7(2) + 10 = 4 – 14 + 10 = 0.

As we have seen, there can be 0, 1, or 2 solutions to a quadratic equation, depending on whether the expression inside the square root sign, (b² - 4ac), is positive, negative, or zero.

To work out the number of roots a qudratic ax²​+bx+c=0 you need to compute the discriminant (b²​-4ac). If the discrimant is less than 0, then the quadratic has no real roots. If the discriminant is equal to zero then the quadratic has equal roosts. If the discriminant is more than zero then it has 2 distinct roots.

The graph of a quadratic function is a parabola. The zeros of a parabola are the points on the parabola that intersect the line y = 0 (the horizontal x-axis). Since these points occur where y = 0, the zeros of a quadratic function occur where f(x) = 0, or at the x-values that make a x 2 + b x + c = 0 a true equation.

Factoring is the first of the three methods of solving quadratic equations. It is often the fastest way to solve a quadratic equation, so usually should be attempted before any other method. This method relies on the fact that if two expressions multiply to zero, then at least one of them must be zero.

Set the equation equal to zero. If the quadratic side is factorable, factor, then set each factor equal to zero. If the quadratic equation involves a SQUARE and a CONSTANT (no first degree term), position the square on one side and the constant on the other side. Then take the square root of both sides.

Answer: There are various methods by which you can solve a quadratic equation such as: factorization, completing the square, quadratic formula, and graphing. These are the four general methods by which we can solve a quadratic equation.

For any quadratic equation ax² + bx + c = 0 whose roots are α and β, the sum of the roots, α + β = -b/a. the product of the roots, α × β = c/a.

How to find roots of quadratic equation shortcut? ›

Let ax2+bx+c=0 a x 2 + b x + c = 0 be the quadratic. I usually start by looking if: 1) a+b+c=0 a + b + c = 0 then the roots are 1 and c/a . Example: 33x2−41x+8=0 33 x 2 − 41 x + 8 = 0 has 1 and 8/33 as solutions.

The quadratic equation formula to solve the equation ax² + bx + c = 0 is x = [-b ± √(b² - 4ac)]/2a. Here we obtain the two values of x, by applying the plus and minus symbols in this formula. Hence the two possible values of x are [-b + √(b² - 4ac)]/2a, and [-b - √(b² - 4ac)]/2a.

Real roots of a polynomial equation are solutions that belong to the set of real numbers. In the context of quadratic equations like ax²+bx+c=0, real roots can be found using the quadratic formula: ​​x = (−b ± b²−4ac)​​/2a. For example, consider the equation x²−4=0. The coefficients are a = 1, b = 0, and c = −4.

The roots of an equation are the "solutions" or numerical values equal to the variable of the given equation. A quadratic equation is an equation in the form of a x 2 + b x + c = 0 where 'a' and 'b' are coefficients, and 'c' is a constant that must be greater than 0.

A quadratic equation in its standard form is represented as: ax² + bx + c = 0, where a, b and c are real numbers such that a ≠ 0 and x is a variable. The number of roots of a polynomial equation is equal to its degree. So, a quadratic equation has two roots.

Answer and Explanation:

The result is a number with infinite decimals. Therefore, the sets to which belongs are: Irrational numbers and real numbers.

The square roots of numbers that are not a perfect square are members of the irrational numbers. This means that they can't be written as the quotient of two integers. The decimal form of an irrational number will neither terminate nor repeat.

Because -√3 written as a decimal number does not stop or repeat, it belongs to the set of irrational numbers. All irrational numbers are real numbers, so -√3 does belong to the set of real numbers.In summary,-√3 belongs to the following sets: irrational numbers and real numbers.