The equation is |x|2-3|x|+2=0
If x>0
then the equation becomes
x2-3x+2=0
(x-2)(x-1)=0
x=1,2
We get two values for x.
If x<0, then the equation is again
x2-3x+2=0
We again get two values.
Therefore, the total number of solutions=4.
The discriminant must be a perfect square or a square of a rational number.
Technically,no. A radical equation has a radical (Square root) in it, and has two solutions because the square root can be positive or negative.
This is a quadratic equation which will have two solutions: X2 = 4x+5 Rearrange the equation: x2-4x-5 = 0 Factor the equation: (x+1)(x-5) = 0 So the solutions are: x = -1 or x = 5
An equation can be determine to have no solution or infinitely many solutions by using the square rule.
Yes. Quite often, if you don't, you'll lose solutions. That is, the transformed equation - after taking square roots - will have less solutions than the original equation.
The discriminant must be a perfect square or a square of a rational number.
A positive number has two square roots, that is, there are two solutions to an equation like x2 = 100. The "principal square root" refers to the positive solution.
on these problems you have o say it out to figure it out three times 3times something the square of a number x so the answer is 3x2
Technically,no. A radical equation has a radical (Square root) in it, and has two solutions because the square root can be positive or negative.
This is a quadratic equation which will have two solutions: X2 = 4x+5 Rearrange the equation: x2-4x-5 = 0 Factor the equation: (x+1)(x-5) = 0 So the solutions are: x = -1 or x = 5
An equation can be determine to have no solution or infinitely many solutions by using the square rule.
The two solutions are coincident.
Yes. Quite often, if you don't, you'll lose solutions. That is, the transformed equation - after taking square roots - will have less solutions than the original equation.
There are no real solutions to this equation because you cannot take the square root of a negative number. However,x2 + 4 = 0x2 = -4sqrt(x2) = sqrt(-4)x = 2i, -2ihere are the imaginary solutions.
Two cases in which this can typically happen (there are others as well) are: 1. The equation includes a square. Example: x2 = 25; the solutions are 5 and -5. 2. The equation includes an absolute value. Example: |x| = 10; the solutions are 10 and -10.
It often helps to isolate the radical, and then square both sides. Beware of extraneous solutions - the new equation may have solutions that are not part of the solutions of the original equation, so you definitely need to check any purported solutions with the original equation.
x2 -y2 =16 This is an equation that describes your problem. We can write this equation as (1/16)x2 -(1/16)y2 =1 You may recognize this as the equation whose graph is a hyperbola. So there are an infinite number of solutions.