# What is meant by real and distinct roots?

The discriminant Δ The equation has two solutions. and. The two solutions might be the same or different (

**distinct**),**real**numbers or not**real**numbers. The nature of the**roots**of the equation (a**root**is another word for solution) clearly depends on the value of the expression under the square**root**sign, .A.

### What does it mean to have real roots?

If the discriminant of a quadratic function

**is**greater than zero, that function has two**real roots**(x-intercepts). Taking the square**root**of a positive**real**number**is**well defined, and the two**roots**are given by, An example of a quadratic function with two**real roots is**given by, f(x) = 2x^{2}− 11x + 5.#### What does it mean when the discriminant is negative?

The radicand of the quadratic formula is the**discriminant**. In other words the**discriminant**is b^{2}- 4ac. (3)**If**b^{2}- 4ac < 0 (in other words the**discriminant**is a**negative**number), then the quadratic equation will have no Real solutions.#### What is the quadratic formula?

In elementary algebra, the**quadratic formula**is the solution of the**quadratic equation**. There are other ways to**solve**the**quadratic equation**instead of using the**quadratic formula**, such as factoring, completing the square, or graphing.#### How do you solve a quadratic equation?

**Method 2****Using the Quadratic Formula**- Combine all of the like terms and move them to one side of the equation.
- Write down the quadratic formula.
- Identify the values of a, b, and c in the quadratic equation.
- Substitute the values of a, b, and c into the equation.
- Do the math.
- Simplify the square root.

B.

### How do you find the roots of a quadratic equation?

**Method 2**

**Finding Roots by Factoring**

- Start with an equation in the quadratic form.
- Set your equation up in the form (x + _)(x + _) = 0.
- Find the factors of your "C" term.
- Find the two factors of C that add up to your "B" term.
- Fill in the spaces in your factored equation.
- Solve for both "x" values.

#### How do you find the factors of a quadratic equation?

**Solution**- First, factorise the quadratic equation x
^{2}- 9x + 20 = 0. - Find two numbers which add up to 9 and multiply to give 20. These numbers are 4 and 5.
- Now find the value x so that when these brackets are multiplied together the answer is 0.
- You can check these answers by substitutuing 4 and 5 in to the equation:

- First, factorise the quadratic equation x
#### Are real numbers complex?

A**complex number**is a**number**that can be expressed in the form a + bi, where a and b are**real numbers**, and i is a solution of the equation x^{2}= −1. Because no**real number**satisfies this equation, i is called an imaginary**number**.#### What are the zeros of the function?

In other words, a "zero" of a**function**is an input value that produces an output of . . If the**function**maps real numbers to real numbers, its**zeros**are the -coordinates of the points where its graph meets the x-axis. An alternative name for such a point in this context is an -intercept.

C.

### What is a real root in math?

The

**real**number x=a is a**root**of the polynomial f(x) if and only if. When we see a graph of a polynomial,**real roots**are x-intercepts of the graph of f(x). Let's look at an example: The graph of the polynomial above intersects the x-axis at (or close to) x=-2, at (or close to) x=0 and at (or close to) x=1.#### Which polynomial function has an end behavior of up and down?

Since the**leading**coefficient of this odd-degree polynomial is positive, then its end-behavior is going to mimic that of a positive cubic. Therefore, the end-behavior for this polynomial will be: "Down" on the**left**and "up" on the right.#### What is the quadratic formula?

In elementary algebra, the**quadratic formula**is the solution of the**quadratic equation**. There are other ways to**solve**the**quadratic equation**instead of using the**quadratic formula**, such as factoring, completing the square, or graphing.#### What is a rational root?

The**Rational Roots**Test (also known as**Rational**Zeros Theorem) allows us to find all possible**rational roots**of a polynomial. Suppose “a” is**root**of the polynomial P (x) that means P (a) = 0. In other words, if we substitute “a” into the polynomial P (x) and get zero it means that the input value is a**root**.

Updated: 28th September 2018