Quadratic Equations
GCE Mathematics

A rectangular garden has a length that is 3 m more than twice its width. If the area of the garden is 44 m², find: (a) Write down a quadratic equation in terms of the width, x, of the garden. [3 marks…

Given that α and β are the roots of the quadratic equation 3x² - 5x + 1 = 0: (a) Write down the values of (α + β) and αβ. [2 marks] (b) Find the value of: (i) α² + β² [3 marks] (ii) α³ + β³ …

The product of the roots of the equation 2x² + 5x - 3 = 0 is:

Using the quadratic formula, solve 2x² - 3x - 2 = 0. The roots are:

Which of the following is a root of the quadratic equation x² - 5x + 6 = 0?

Find the values of k for which the equation x² - 6x + k = 0 has equal roots.

A quadratic equation has roots α and β such that α + β = 3 and αβ = -10. Which of the following is the equation?

If one root of the equation x² + px + 12 = 0 is 4, find the value of p.

Find the sum of the roots of the equation 3x² - 7x + 2 = 0.