Pergunta

A quadratic can have __ solution(s). Select all that apply. no or zero infinitely many cubic two one three
Solução

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AntónioElite · Tutor por 8 anos
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A quadratic can have no or zero, one, or two solutions.
Explicação
## Step 1
A quadratic equation is a second-degree polynomial equation in a single variable x, with a non-zero coefficient for x^2. The general form is ax^2+bx+c=0, where x represents an unknown, and a, b, and c are constants with a ≠ 0.
## Step 2
The solutions of a quadratic equation are the values of x that make the equation true. These solutions can be found using the quadratic formula, factoring, completing the square, or graphing.
## Step 3
The number of solutions of a quadratic equation depends on the discriminant, which is the part under the square root in the quadratic formula. The discriminant is b^2 - 4ac.
## Step 4
If the discriminant is greater than zero, the quadratic equation has two distinct real solutions.
## Step 5
If the discriminant is equal to zero, the quadratic equation has one real solution.
## Step 6
If the discriminant is less than zero, the quadratic equation has no real solutions.
## Step 7
Therefore, a quadratic equation can have no or zero solutions, one solution, or two solutions. It cannot have infinitely many solutions, cubic solutions, or three solutions.
A quadratic equation is a second-degree polynomial equation in a single variable x, with a non-zero coefficient for x^2. The general form is ax^2+bx+c=0, where x represents an unknown, and a, b, and c are constants with a ≠ 0.
## Step 2
The solutions of a quadratic equation are the values of x that make the equation true. These solutions can be found using the quadratic formula, factoring, completing the square, or graphing.
## Step 3
The number of solutions of a quadratic equation depends on the discriminant, which is the part under the square root in the quadratic formula. The discriminant is b^2 - 4ac.
## Step 4
If the discriminant is greater than zero, the quadratic equation has two distinct real solutions.
## Step 5
If the discriminant is equal to zero, the quadratic equation has one real solution.
## Step 6
If the discriminant is less than zero, the quadratic equation has no real solutions.
## Step 7
Therefore, a quadratic equation can have no or zero solutions, one solution, or two solutions. It cannot have infinitely many solutions, cubic solutions, or three solutions.
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