# 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) = 2x2− 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 b2 - 4ac. (3) If b2 - 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
1. Combine all of the like terms and move them to one side of the equation.
2. Write down the quadratic formula.
3. Identify the values of a, b, and c in the quadratic equation.
4. Substitute the values of a, b, and c into the equation.
5. Do the math.
6. Simplify the square root.
B.

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

Method 2 Finding Roots by Factoring
2. Set your equation up in the form (x + _)(x + _) = 0.
3. Find the factors of your "C" term.
4. Find the two factors of C that add up to your "B" term.
5. Fill in the spaces in your factored equation.
6. Solve for both "x" values.
• #### How do you find the factors of a quadratic equation?

Solution
1. First, factorise the quadratic equation x2- 9x + 20 = 0.
2. Find two numbers which add up to 9 and multiply to give 20. These numbers are 4 and 5.
3. Now find the value x so that when these brackets are multiplied together the answer is 0.
4. You can check these answers by substitutuing 4 and 5 in to the equation:
• #### 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 x2 = −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: 2nd October 2019

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