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What is true of the discriminant when the two real number solutions to a quadratic equation are rational numbers?
The discriminant must be a perfect square or a square of a rational number.
What happens when there is negative under the square root in a quadratic equation?
When there is a negative number under the square root in a quadratic equation, it indicates that the equation has no real solutions. Instead, it results in complex or imaginary solutions, as the square root of a negative number involves the imaginary unit (i). This situation occurs when the discriminant (the part under the square root in the quadratic formula) is negative. Consequently, the quadratic graph does not intersect the x-axis, indicating no real roots.
How do you solve a square root equation?
To solve a square root equation, first isolate the square root term on one side of the equation. Then, square both sides to eliminate the square root. After squaring, solve the resulting equation for the variable. Finally, check your solutions to ensure they are valid, as squaring can introduce extraneous solutions.
How is a radical equation similar to a linear equation?
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.
The Square of a number is 5 more than 4 times the number. Find the number that makes the sentence true.?
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
What is true of the discriminant when the two real number solutions to a quadratic equation are rational numbers?
The discriminant must be a perfect square or a square of a rational number.
What is the principal square root of a positive 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.
What happens when there is negative under the square root in a quadratic equation?
When there is a negative number under the square root in a quadratic equation, it indicates that the equation has no real solutions. Instead, it results in complex or imaginary solutions, as the square root of a negative number involves the imaginary unit (i). This situation occurs when the discriminant (the part under the square root in the quadratic formula) is negative. Consequently, the quadratic graph does not intersect the x-axis, indicating no real roots.
How do you solve a square root equation?
To solve a square root equation, first isolate the square root term on one side of the equation. Then, square both sides to eliminate the square root. After squaring, solve the resulting equation for the variable. Finally, check your solutions to ensure they are valid, as squaring can introduce extraneous solutions.
What does 3 times the square of a number x means?
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
How is a radical equation similar to a linear equation?
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.
The Square of a number is 5 more than 4 times the number. Find the number that makes the sentence true.?
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
Explain how to identify whether an equation has no solution or infinitely many solutions?
An equation can be determine to have no solution or infinitely many solutions by using the square rule.
What is true about the solutions of a quadratic equation when the radicand of the quadratic formula is a perfect square?
The two solutions are coincident.
Do you need to put a plus or minus sign in front of a square root answer you get from finding the inverse of a quadratic equation?
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.
What is the solution set to the equation x2 plus 4 equals 0?
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.
When does a equation have two 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.
