Math / Algebra

QuestionHow many solutions can a quadratic have?
1,2, or 3 none, 1, or 2 none or 2 1 or 2

Studdy Solution

STEP 1

1. We are considering solutions in the context of real numbers.
2. The quadratic equation is in the standard form $ax^2 + bx + c = 0$ .

STEP 2

1. Understand the nature of solutions for a quadratic equation.
2. Use the discriminant to determine the number of solutions.
3. Conclude the possible number of solutions.

STEP 3

A quadratic equation can have different numbers of solutions based on its discriminant, which is given by $b^2 - 4ac$ .

STEP 4

The discriminant $b^2 - 4ac$ determines the nature of the roots: - If $b^2 - 4ac > 0$ , there are 2 distinct real solutions. - If $b^2 - 4ac = 0$ , there is exactly 1 real solution (a repeated root). - If $b^2 - 4ac < 0$ , there are no real solutions (the solutions are complex).

STEP 5

Based on the discriminant, a quadratic equation can have: - None (0), 1, or 2 real solutions.
The correct choice is:
$\boxed{\text{none, 1, or 2}}$

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QuestionHow many solutions can a quadratic have?
1,2, or 3 none, 1, or 2 none or 2 1 or 2

Studdy Solution

STEP 1

1. We are considering solutions in the context of real numbers.
2. The quadratic equation is in the standard form $ax^2 + bx + c = 0$ .

STEP 2

1. Understand the nature of solutions for a quadratic equation.
2. Use the discriminant to determine the number of solutions.
3. Conclude the possible number of solutions.

STEP 3

A quadratic equation can have different numbers of solutions based on its discriminant, which is given by $b^2 - 4ac$ .

STEP 4

The discriminant $b^2 - 4ac$ determines the nature of the roots: - If $b^2 - 4ac > 0$ , there are 2 distinct real solutions. - If $b^2 - 4ac = 0$ , there is exactly 1 real solution (a repeated root). - If $b^2 - 4ac < 0$ , there are no real solutions (the solutions are complex).

STEP 5

Based on the discriminant, a quadratic equation can have: - None (0), 1, or 2 real solutions.
The correct choice is:
$\boxed{\text{none, 1, or 2}}$

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QuestionHow many solutions can a quadratic have?1,2, or 3 none, 1, or 2 none or 2 1 or 2

Studdy Solution

STEP 1

1. We are considering solutions in the context of real numbers.2. The quadratic equation is in the standard form ax2+bx+c=0 ax^2 + bx + c = 0 ax2+bx+c=0.

STEP 2

1. Understand the nature of solutions for a quadratic equation.2. Use the discriminant to determine the number of solutions.3. Conclude the possible number of solutions.

STEP 3

A quadratic equation can have different numbers of solutions based on its discriminant, which is given by b2−4ac b^2 - 4ac b2−4ac.

STEP 4

STEP 5

Based on the discriminant, a quadratic equation can have: - None (0), 1, or 2 real solutions.The correct choice is:none, 1, or 2 \boxed{\text{none, 1, or 2}} none, 1, or 2​

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionHow many solutions can a quadratic have?
1,2, or 3 none, 1, or 2 none or 2 1 or 2

1. We are considering solutions in the context of real numbers.
2. The quadratic equation is in the standard form $ax^2 + bx + c = 0$ .

1. Understand the nature of solutions for a quadratic equation.
2. Use the discriminant to determine the number of solutions.
3. Conclude the possible number of solutions.

A quadratic equation can have different numbers of solutions based on its discriminant, which is given by $b^2 - 4ac$ .

Based on the discriminant, a quadratic equation can have: - None (0), 1, or 2 real solutions.
The correct choice is:
$\boxed{\text{none, 1, or 2}}$