📐 Quadratic Equations and Roots

Master solving quadratic equations and understanding roots using multiple methods and properties. **What you'll learn:** - Solve quadratic equations by factorisation, completing the square, and the quadratic formula - Identify the nature of roots using the discriminant - Apply Vieta's formulas to relate roots and coefficients - Solve real-world problems modelled by quadratic equations

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Questions in this quiz

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Question 1
Which of the following is a quadratic equation?
Question 2
The equation $x^2 = 25$ has exactly one real root.
Question 3
The sum of roots of the equation $3x^2 - 12x + 5 = 0$ is ___.
Question 4
What is the discriminant of the equation $x^2 - 4x + 4 = 0$ ?
Question 5
If the discriminant of a quadratic equation is negative, the equation has two distinct imaginary roots.
Question 6
Factorise: $x^2 + 7x + 12 = (x + ___)(x + ___)$ .
Question 7
Using the quadratic formula, solve $2x^2 - 5x + 2 = 0$ . What are the roots?
Question 8
The equation $x^2 - 6x + 9 = 0$ has two distinct real roots.
Question 9
A ball is thrown upwards with initial velocity 20 m/s. Its height after $t$ seconds is $h = 20t - 5t^2$ . At what time does it return to ground level (where $h = 0$ )?
Question 10
If the product of roots of $kx^2 + 3x + 5 = 0$ is $\frac{5}{2}$ , what is the value of $k$ ?