Quadratic Equations

Math ⇒ Algebra

Quadratic Equations starts at 8 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Quadratic Equations. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.

See sample questions for grade 8

Find the roots of the equation x² + 2x - 8 = 0.

If a quadratic equation has two distinct real roots, what can you say about its discriminant?

If the product of the roots of a quadratic equation is negative, what can you say about the signs of the roots?

If the quadratic equation x² + bx + 12 = 0 has roots 3 and -4, what is the value of b?

If the roots of a quadratic equation are 4 and -3, what is the equation in standard form?

If the roots of a quadratic equation are both negative, what can you say about the signs of b and c in ax² + bx + c = 0 (a > 0)?

If the sum of the roots of a quadratic equation is 7 and the product is 10, what is the equation?

A ball is thrown upwards from the ground and its height h (in meters) after t seconds is given by h = -4.9t² + 19.6t. After how many seconds will the ball return to the ground?

If the discriminant of a quadratic equation is negative, the equation has (1) two real roots (2) one real root (3) two complex roots (4) no roots

Which method can be used to solve any quadratic equation? (1) Factoring (2) Completing the square (3) Quadratic formula (4) All of the above

Which of the following equations has a discriminant equal to zero? (1) x² + 2x + 1 = 0 (2) x² + 4x + 5 = 0 (3) x² - 5x + 6 = 0 (4) x² - 2x + 1 = 0

Which of the following equations has equal roots? (1) x² + 4x + 4 = 0 (2) x² + 2x + 1 = 0 (3) x² + 5x + 6 = 0 (4) x² + 3x + 2 = 0

Fill in the blank: The axis of symmetry of the parabola y = 2x² - 8x + 3 is x = __________.

Fill in the blank: The maximum or minimum value of a quadratic function occurs at the __________ of the parabola.

Fill in the blank: The product of the roots of ax² + bx + c = 0 is __________.

Fill in the blank: The quadratic equation x² - 6x + 9 = 0 can be written as (x - __________)² = 0.

True or False: The coefficient 'a' in ax² + bx + c = 0 must not be zero.

True or False: The equation x² - 2x + 1 = 0 can be written as (x - 1)² = 0.

True or False: The equation x² - 4x + 4 = 0 has only one solution.

True or False: The equation x² + 1 = 0 has real solutions.