Quadratic Equations
Math ⇒ Algebra
Quadratic Equations starts at 8 and continues till grade 12.
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See sample questions for grade 10
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?
A quadratic equation has roots 5 and -2. What is the sum and product of the roots?
A quadratic equation has roots α and β. If α + β = 7 and αβ = 10, write the equation.
Find the roots of the equation x² + 2x + 1 = 0.
If one root of the equation x² + px + 12 = 0 is 3, what is the value of p?
If the discriminant of a quadratic equation is negative, what type of roots does it have?
If the equation x² + 6x + k = 0 has real roots, what is the range of values for k?
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?
Which of the following equations has complex roots?
(1) x² - 4x + 4 = 0
(2) x² + 2x + 5 = 0
(3) x² - 5x + 6 = 0
(4) x² - 1 = 0
Which of the following equations has real and equal roots?
(1) x² + 4x + 4 = 0
(2) x² + 2x + 5 = 0
(3) x² - 3x + 2 = 0
(4) x² + x + 1 = 0
Which of the following equations is a quadratic equation?
(1) x² + 3x + 2 = 0
(2) 2x + 5 = 0
(3) x³ - 4x = 0
(4) 5x - 7 = 2x²
Which of the following is a quadratic equation in one variable?
(1) x² + y² = 1
(2) x² + 2x = 0
(3) x + y = 0
(4) x³ + 2x = 0
Fill in the blank: The axis of symmetry of the parabola y = ax² + bx + c is x = __________.
Fill in the blank: The graph of a quadratic equation is called a __________.
Fill in the blank: The product of the roots of the equation ax² + bx + c = 0 is __________.
Fill in the blank: The quadratic equation x² + bx + c = 0 can be solved by __________ the square.
True or False: The coefficient 'a' in ax² + bx + c = 0 must not be zero.
True or False: The graph of every quadratic equation is a straight line.
True or False: The product of the roots of x² + 6x + 9 = 0 is 9.
True or False: The quadratic equation x² + 1 = 0 has real roots.
