What is a quadratic equation with 2 solutions?

If the discriminant is positive then there are two distinct solutions. For example, in the quadratic equation 4×2 + 26x + 12 = 0, its discriminant is equals to b2 − 4ac = (26)2 − 4(4)(12) = 484 which is positive and so the equation has two real solutions.

What’s an example of a quadratic equation with two real solutions?

Notice that the discriminant of f(x) is zero, b2 −4ac = (12)2− 4 · −4 · −9 = 144 − 144 = 0. An example of a quadratic function with two real roots is given by, f(x) = 2×2− 11x + 5.

Can 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 know if a quadratic equation has two solutions?

Talk the Talk Given a quadratic equation ax2 + bx + c = 0, plug the coefficients into the expression b2 – 4ac to see what results: 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.

What is an equation with two solutions?

A quadratic equation has two solutions. Either two distinct real solutions, one double real solution or two imaginary solutions. There are several methods you can use to solve a quadratic equation: Factoring.

Can a quadratic equation have more than 2 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.

How do you find two real solutions?

If the value of the discriminant is positive, there are two real solutions for x, meaning the graph of the solution has two distinct x-intercepts. If the value of the discriminant is zero, there is one real solution for x, meaning the graph of the solution has one x-intercept.

What are the solutions of the quadratic equation 2×2 − 4x 3?

Two solutions were found : x =(4-√-8)/4=1-i/2√ 2 = 1.0000-0.7071i.

Which are the solutions of the quadratic equation x2 7x 4?

Summary: The solution of the quadratic equation x2 = 7x + 4 is x = [7 ± √65]/2.

What is the solution set of the following equation 6×2 13x 5?

Summary: The solution set of the following equation 6×2 = 13x + 5 is (5/2, -1/3).

How many solutions are in a quadratic equation?

2 solutions
As we have seen, there can be 0, 1, or 2 solutions to a quadratic equation, depending on whether the expression inside the square root sign, (b2 – 4ac), is positive, negative, or zero. This expression has a special name: the discriminant.

What if a quadratic equation has more than 2 roots?

If a quadratic equation ax2+bx+c=0 has more than two roots, then it is an identity i.e. it is true for all values of x and a=b=c=0. What is a proof of this? When the equation has more than two roots, it means that it intercepts the x-axis more than two times.

What does 2 real solutions mean?

What does two equal solutions mean?

Well the square root of zero is zero so we would essentially be adding zero to negative b in the numerator. Because adding or subtracting zero yields the same response, having a discriminant value of zero would indicate only one real solution. This is often called a “double solution” or “two equal solutions”