Table of Contents

- 1 What is the relationship between the factors and the roots?
- 2 How are a quadratic function roots related to its factors?
- 3 How are the factors of a quadratic related to the zeros or roots of a quadratic?
- 4 What is the difference between roots and factors of a quadratic equation?
- 5 What the difference is between roots solutions and zeros?
- 6 What is the relationship between a root of a polynomial and a factor of a polynomial?

## What is the relationship between the factors and the roots?

The factor theorem states that if x = c is a root, (x – c) is a factor. For example, look at the following roots: If x = –1/2, (x – (–1/2)) is your factor, which you write as (x + 1/2). If x = –3 is a root, (x – (–3)) is a factor, which you write as (x + 3).

It’s factors are (x – 7)(x + 4). The roots are the x-values that make our expression equal 0. In order for x2 – 3x – 28 to equal 0, either of our factors need to equal 0, since 0 times anything is 0.

**What is the relationship between the roots of a quadratic equation?**

The sum of the roots of a quadratic equation is equal to the negation of the coefficient of the second term, divided by the leading coefficient. The product of the roots of a quadratic equation is equal to the constant term (the third term), divided by the leading coefficient.

**What is the relation between roots and coefficients of a quadratic equation?**

Solution: Let α and β be the roots of the given equation. Sometimes the relation between roots of a quadratic equation is given and we are asked to find the condition i.e., relation between the coefficients a, b and c of quadratic equation. This is easily done using the formula α + β = -ba and αβ = ca.

The zero product principle states that if two factors multiply to zero, at least one of the factors must equal zero. The values that make a polynomial equal zero are known as the roots. To find the zeros/roots of a quadratic: factor the equation, set each of the factors to 0, and solve for x.

### What is the difference between roots and factors of a quadratic equation?

If we set this equal to a number c, we have a quadratic equation. you can say (x – a) and (x – b) are factors. But the numbers a and b are the roots. The root a is a number that you can substitute in for x and get a true statement.

**Where are the roots in a quadratic equation?**

The roots of a function are the x-intercepts. By definition, the y-coordinate of points lying on the x-axis is zero. Therefore, to find the roots of a quadratic function, we set f (x) = 0, and solve the equation, ax2 + bx + c = 0.

**What is the relationship between zeros and roots?**

A zero ( or root ) of a function is an input, whose corresponding output is zero. Let P be a polynomial, and let c be an input to P .

## What the difference is between roots solutions and zeros?

A root of an equation is a value at which the equation is satisfied. Roots the equation f(x)= x3+ x2– 3x – ex=0 are the x values of the points A, B, C and D. At these points, the value of the function becomes zero; therefore, the roots are called zeroes.

## What is the relationship between a root of a polynomial and a factor of a polynomial?

The Fundamental Theorem of Algebra tells you that the polynomial has at least one root. The Factor Theorem tells you that if r is a root then (x−r) is a factor. But if you divide a polynomial of degree n by a factor (x−r), whose degree is 1, you get a polynomial of degree n−1.