General Quadratic Equations MCQ

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Question 1: What is the standard form of a quadratic equation?

A) ax^2 + bx + c = 0

B) ax^2 + c = 0

C) x^2 + bx = 0

D) ax^2 + b = 0

Question 2: What is the discriminant of a quadratic equation ax^2 + bx + c = 0?

A) b^2 - ac

B) b^2 - 4ac

C) a^2 - 4bc

D) b^2 + 4ac

Question 3: For which condition does a quadratic equation have real roots?

A) b^2 - 4ac < 0

B) b^2 - 4ac = 0

C) b^2 - 4ac ≥ 0

D) b^2 - 4ac > 0

Question 4: Which of the following is used to solve a quadratic equation?

A) Completing the square

B) Graphing

C) Factoring

D) Quadratic formula

Question 5: What is the quadratic formula?

A) x = (-b ± √(b² - 4ac)) / 2a

B) x = (b ± √(b² + 4ac)) / 2a

C) x = (-b ± √(4ac - b²)) / 2a

D) x = (-b ± √(c² - 4ac)) / 2a

Question 6: What type of roots does a quadratic equation with a negative discriminant have?

A) Real roots

B) Double roots

C) Complex roots

D) No roots

Question 7: What is the sum of the roots of the equation ax^2 + bx + c = 0?

A) c/a

B) -b/a

C) b/a

D) a/b

Question 8: If the discriminant of a quadratic equation is zero, how many real roots does it have?

A) One real root

B) Two real roots

C) No real roots

D) Infinitely many real roots

Question 9: Which of the following is the factorization of x² - 5x + 6 = 0?

A) (x - 1)(x - 6) = 0

B) (x + 2)(x + 3) = 0

C) (x - 2)(x - 3) = 0

D) (x + 1)(x + 6) = 0

Question 10: In the equation ax² + bx + c = 0, what does b represent?

A) The constant term

B) The coefficient of x

C) The coefficient of x²

D) The discriminant

Question 11: Which method is used to solve a quadratic equation?

A) Multiplication

B) Addition

C) Substitution

D) Factoring or quadratic formula

Question 12: Where is the vertex of a parabola represented by the quadratic equation ax² + bx + c?

A) x = b/(2a)

B) x = -a/(2b)

C) x = -b/(2a)

D) x = c/(2b)

Question 13: What does the sign of 'a' in the quadratic equation ax² + bx + c = 0 determine?

A) The discriminant

B) The direction of the parabola

C) The roots of the equation

D) The sum of the roots

Question 14: Which of the following represents the general solution to a quadratic equation?

A) x = (-b ± √b²)/2a

B) x = -b ± √(b² + 4ac)

C) x = √(b² - 4ac)

D) x = (-b ± √(b² - 4ac)) / 2a

Question 15: What are the solutions to the equation x² - 4x + 3 = 0?

A) x = 1, x = 3

B) x = 2, x = 3

C) x = -1, x = -3

D) x = 4, x = 5

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