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What is a quadratic equation?

A quadratic equation is a polynomial equation of degree 2, where the highest power of the variable is 2.

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What is the general form of a quadratic equation?

The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

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How many solutions can a quadratic equation have?

A quadratic equation can have either two distinct solutions, one repeated solution, or no real solutions.

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What is the discriminant of a quadratic equation?

The discriminant of a quadratic equation is the expression b^2 - 4ac, which determines the nature of the solutions.

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How can you determine the nature of the solutions based on the discriminant?

If the discriminant is positive, the quadratic equation has two distinct real solutions. If it is zero, the equation has one repeated real solution. If it is negative, the equation has no real solutions.

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Solve the quadratic equation: x^2 - 5x + 6 = 0.

Factoring the equation, we get (x - 2)(x - 3) = 0. Therefore, the solutions are x = 2 and x = 3.

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Solve the quadratic equation: 2x^2 + 7x - 3 = 0.

Using the quadratic formula, we get x = (-7 ± √(7^2 - 4(2)(-3))) / (2(2)). Simplifying, we get x = (-7 ± √(49 + 24)) / 4. Therefore, the solutions are x = (-7 + √73) / 4 and x = (-7 - √73) / 4.

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Solve the quadratic equation: 3x^2 - 2x + 1 = 0.

Using the quadratic formula, we get x = (2 ± √(2^2 - 4(3)(1))) / (2(3)). Simplifying, we get x = (2 ± √(-8)) / 6. Since the discriminant is negative, the equation has no real solutions.

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Create quizThis set of practice questions will test your understanding of quadratic equations. Each question is followed by a detailed answer explanation to help you learn and improve.

32 questions

English

11-07-2023

University / UoL / Economics / Miscellaneous test questions on quadratic equation

John U. Ekpenyong

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