What is a quadratic equation with 2 solutions?
It is called the Discriminant, because it can “discriminate” between the possible types of answer: when b2 − 4ac is positive, we get two Real solutions. when it is zero we get just ONE real solution (both answers are the same) when it is negative we get a pair of Complex solutions.
What are the solutions to the quadratic equation x2 16 0?
A. The only solution of the equation x2 + bx + 16 = 0 is x = 4.
How do you know if an equation has two solutions?
The discriminant is the part under the square root in the quadratic formula, b²-4ac. If it is more than 0, the equation has two real solutions. If it’s less than 0, there are no solutions. If it’s equal to 0, there is one solution.
Do quadratic equations always have 2 real solutions?
A quadratic equation has two solutions. Either two distinct real solutions, one double real solution or two imaginary solutions. All methods start with setting the equation equal to zero.
How do you tell if a quadratic has no solution?
If you get a positive number, the quadratic will have two unique solutions. If you get 0, the quadratic will have exactly one solution, a double root. If you get a negative number, the quadratic will have no real solutions, just two imaginary ones.
Why do quadratic equations have two solutions?
1 Answer. A quadratic expression can be written as the product of two linear factors and each factor can be equated to zero, So there exist two solution.
How do you solve quadratic equations?
Solving Quadratic EquationsPut all terms on one side of the equal sign, leaving zero on the other side.Factor.Set each factor equal to zero.Solve each of these equations.Check by inserting your answer in the original equation.
What is the first step in solving the quadratic equation x2 9/16 quizlet?
take the square root of both sides of the equation. add 9/16 to both sides of the equation.
What is x2 16?
x2=16. What is x? in my view the question is x^2=16,so the answer is x=4 or x=-4.
What is an equation with no solution?
The solution x = 0 means that the value 0 satisfies the equation, so there is a solution. “No solution” means that there is no value, not even 0, which would satisfy the equation. If you substitute these values into the original equation, you’ll see that they do not satisfy the equation.
Can a quadratic equation have 3 solutions?
Therefore, our assumption that a quadratic equation has three distinct real roots is wrong. Hence, every quadratic equation cannot have more than 2 roots. Note: If a condition in the form of a quadratic equation is satisfied by more than two values of the unknown then the condition represents an identity.
What are some real life applications of quadratic equations?
For a parabolic mirror, a reflecting telescope or a satellite dish, the shape is defined by a quadratic equation. Quadratic equations are also needed when studying lenses and curved mirrors. And many questions involving time, distance and speed need quadratic equations.
What is the point of quadratic equations?
Quadratic equations are actually used in everyday life, as when calculating areas, determining a product’s profit or formulating the speed of an object. Quadratic equations refer to equations with at least one squared variable, with the most standard form being ax² + bx + c = 0.