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 11

A ball is thrown upwards and its height h (in meters) after t seconds is given by h = -5t² + 20t + 2. What is the maximum height reached by the ball?

Find the discriminant of the equation 2x² + 3x - 2 = 0.

Given the equation 4x² - 4x + 1 = 0, find its roots.

Given the equation x² - 6x + 9 = 0, what is the nature of its roots?

If one root of the equation x² + px + 12 = 0 is 3, what is the value of p?

If the quadratic equation 2x² + kx + 8 = 0 has equal roots, what is the value of k?

If the roots of a quadratic equation are 4 and -2, write the equation in standard form.

If the roots of the equation x² + bx + c = 0 are reciprocal to each other, what is the value of c?

If the roots of the quadratic equation x² + bx + 16 = 0 are both negative, what can you say about the value of b?

If the sum and product of the roots of a quadratic equation are 7 and 12 respectively, write the equation.

Solve for x: 3x² - 12 = 0.

Solve for x: x² + 2x + 5 = 0.

Solve the quadratic equation x² - 5x + 6 = 0.

A quadratic equation has roots α and β such that α + β = 5 and α² + β² = 13. Find the equation.

Given the equation x² + 2x + k = 0, for which values of k will the roots be complex and conjugate?

Given the quadratic equation 2x² + (k-3)x + k = 0, for what value(s) of k does the equation have exactly one real root?

If the quadratic equation 3x² + 7x + k = 0 has one root twice the other, find the value of k.

If the roots of the quadratic equation x² + px + q = 0 differ by 4, express p in terms of q.