two real
The complex roots of an equation is any solution to that equation which cannot be expressed in terms of real numbers. For example, the equation 0 = x² + 5 does not have any solution in real numbers. But in complex numbers, it has solutions.
A cubic has from 1 to 3 real solutions. The fact that every cubic equation with real coefficients has at least 1 real solution comes from the intermediate value theorem. The discriminant of the equation tells you how many roots there are.
It is not to solve so much as to see the number of solutions and whether there is a real solution to the equation. b2 - 4(a)(c) A positive answer = two real solutions. A negative answer = no real solution ( complex solution i ) If zero as the answer there is one real solution.
domain is set of real numbers range is set of real numbers
It has one real solution.
8 = 8v - 4v8 This equation does not have any real solution.
-4
The equation does not have a real number solution. Using the quadratic formula will give it's conjugate pair complex solution.
It has one double solution.
The equation has two real solutions.
3
You should be able to look at this equation, or use the discriminant and know that there are no real roots.
There is one and only one real solution, and no imaginary solutions, of the equation x13 = 1. The solution is x = 1. If x = -1 then x13 = -1, so that does not work. If x = i, then x13 = -i, so that does not work. If x = -i, then x13 = -i, so that does not work.
Is it possible for a quadratic equation to have no real solution? please give an example and explain. Thank you
You are supposed to calculate the so-called discriminant, b2 - 4ac. If the result is positive, the equation has two real solutions; if it is zero, one real solution; if it is negative, no real solution (and two complex solutions). For this particular equation, a = 1, b = -10, and c = 25.
This is an equation of a straight line. A solution for two unknowns requires two (independent) equations; there is only one here. Every point that is on that line is a solution to the equation. So you can let x be any real number and find a corresponding y. This ordered pair (x,y) will be a solution to the equation as well as a point on the graph of the line.