What types of roots or solutions does a quadratic equation have if its discriminant is positive?

A positive discriminant indicates that the quadratic has two distinct real number solutions. A discriminant of zero indicates that the quadratic has a repeated real number solution. A negative discriminant indicates that neither of the solutions are real numbers.

What is a solution of a quadratic equation?

The solutions of the quadratic equation ax2 + bx + c = 0 correspond to the roots of the function f(x) = ax2 + bx + c, since they are the values of x for which f(x) = 0.

Does every quadratic equation have two solutions?

Every quadratic equation has two solutions and can be factorized, but as level of difficulty rises, splitting may not be easy and one may tend to use quadratic formula.

What kind of roots or solutions of the quadratic equation?

Let ax2 + bx + c = 0 be a quadratic equation. If aα2 + bα + c = 0 then α is called a root of the quadratic equation ax2 + bx + c = 0. If aα2 + bα + c = 0 then we say x = α satisfies the equation ax2 + bx + c = 0 and x = α is a solution. Thus, every solution is root.

Why quadratic equation is called quadratic?

We use the word quadratic because “quadra” refers to a square, and the leading term in a quadratic equation is “squared.” This is consistent with calling a degree three polynomial a “cubic” for the leading term represents a cube. The word for an equation with a leading term of x^4 is “quartic.”

Does a quadratic equation have at most two solutions?

Quadratic equations differ from linear equations in that a linear equation has only one solution, while a quadratic equation has at most two solutions. There are some special situations, however, in which a quadratic equation has either one solution or no solutions. We solve quadratic equations using factorisation.

How do you find the solutions to the quadratic equation?

The ” solutions ” to the Quadratic Equation are where it is equal to zero. There are usually 2 solutions (as shown in this graph). And there are a few different ways to find the solutions: Just plug in the values of a, b and c, and do the calculations.

How to solve X = 2 − 3 ± 3 7 ​ ​?

Now solve the equation x = 2 − 3 ± 3 7 ​ ​ when ± is minus. Subtract 3 7 ​ from − 3. The equation is now solved. The equation is now solved. x2+3x-7=0 Two solutions were found : x = (-3-√37)/2=-4.541 x = (-3+√37)/2= 1.541 Step by step solution : Step 1 :Trying to factor by splitting the middle term 1.1 Factoring x2+3x-7

What is the quadratic formula for b2 4ac?

Quadratic Formula: x = −b ± √ (b2 − 4ac) 2a. When the Discriminant ( b2−4ac) is: positive, there are 2 real solutions. zero, there is one real solution. negative, there are 2 complex solutions.

How do you find the original quadratic function with two X values?

If you were given only two x values of the roots then put them into the form that would give you those two x values (when set equal to zero) and multiply to see if you get the original function. For our problem the correct answer is . Use the foil method to get the original quadratic.