Table of Contents
- 1 Can a quadratic equation have 4 solutions?
- 2 How do you find the solution to a quartic equation?
- 3 Can quadratic equations have 3 solutions?
- 4 How many real solutions does have?
- 5 How many solutions can a cubic equation have?
- 6 How many solutions can 2 parabolas have?
- 7 How do you find the number of solutions to a quadratic equation?
- 8 What are quartic equations?
- 9 What is the difference between quadratic equations and complex numbers?
Can a quadratic equation have 4 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.
How do you find the solution to a quartic equation?
Correct answer:
- This is a relatively standard quadratic equation. List and add factors of 18.
- Pull out common factors of each pair, “x” from the first and “6” from the second. \displaystyle x(x+3)+6(x+3)=0.
- Factor again, pulling out “(x+3)” from both terms.
- Set each term equal to zero and solve.
How many solution are there in quadratic equation?
two solutions
A quadratic equation with real or complex coefficients has two solutions, called roots.
Can quadratic equations have 3 solutions?
Therefore, the roots of the given quadratic equation are 2 and -23. Hence, a quadratic equation cannot have more than two distinct roots.
How many real solutions does have?
a positive number inside the square root | zero inside the square root | a negative number inside the square root |
---|---|---|
two real solutions | one (repeated) real solution | two complex solutions |
two distinct x-intercepts | one (repeated) x-intercept | no x-intercepts |
Can you solve quartic equations?
Quartic equations can be solved using a variety of methods. Some can be solved using the difference of square factoring. Some can be made to look like quadratics and then solved like a quadratic. The rational root theorem will show where the possible roots of a equation would exist.
How many solutions can a cubic equation have?
Just as a quadratic equation may have two real roots, so a cubic equation has possibly three. But unlike a quadratic equation which may have no real solution, a cubic equation always has at least one real root.
How many solutions can 2 parabolas have?
If the graphs of the equations do not intersect, then there are no solutions that are true for both equations. If the line intersects the parabola in two places, then there are two solutions that are true for both equations.
How many real solutions are there?
2 real solutions
It determines the number and the type of solutions that a quadratic equation has. If the discriminant is positive, there are 2 real solutions. If it is 0 , there is 1 real repeated solution. If the discriminant is negative, there are 2 complex solutions (but no real solutions).
How do you find the number of solutions to a quadratic equation?
In order to find the number of solutions, we shall split the quadratic equation into 3 cases. Case 1: 2 unique solutions – eg x 2 + 5x + 6 = 0. Has solutions x = 2 and x = 3. Case 2: 1 repeated solution – eg x 2 + 4x + 4 = 0. Has solution x = 2.
What are quartic equations?
Quartic equations are polynomials that have a degree of four. There are several different means of solving quartic equations such as factoring, treating them like quadratics, use of a graphing calculator, and the rational root theorem.
What is the general form of a quadratic equation?
A quadratic equation is an equation that looks like: x 2 + 4x – 2 = 0. The general form of this is written as ax 2 + bx + c = 0, where a, b and c are all numbers, and x is our unknown variable. In the example above, we would have a = 1, b = 4 and c = -2.
What is the difference between quadratic equations and complex numbers?
-Two different solutions: there are two values that satisfy the quadratic equation. For example, x² + x-2 = 0 has two different solutions that are x1 = 1 and x2 = -2. 2.- In the complex numbers When working with complex numbers the quadratic equations always have two solutions which are z1 and z2 where z2 is the conjugate of z1.