Quadratic Equations

Topics in this chapter

• Quadratic Equation Basics
• Solving by Factorisation
• Formula and Completing the Square
• Discriminant and Nature of Roots
• Roots and Coefficients
• Quadratic Word Problems

Cheat sheet

Practice questions

1. Question 1Q-43A16B

   Which of the following is a quadratic equation?

   1. A.$x^2 + 3x + 1 = (x-2)^2$
   2. B.$x(x + 1) + 8 = (x + 2)(x - 2)$
   3. C.$x^3 - 4x^2 - x + 1 = (x - 2)^3$
   4. D.$(x + 2)^3 = 2x(x^2 - 1)$
   See the answer and solution
2. Question 2Q-74126A

   Find the roots of the quadratic equation $\sqrt{2}x^2 + 7x + 5\sqrt{2} = 0$.

   1. A.$-\sqrt{2}, -\frac{5}{\sqrt{2}}$
   2. B.$\sqrt{2}, \frac{5}{\sqrt{2}}$
   3. C.$-\sqrt{2}, \frac{5}{\sqrt{2}}$
   4. D.$\sqrt{2}, -\frac{5}{\sqrt{2}}$
   See the answer and solution
3. Question 3Q-F82EE7

   Find the value of $k$ for which the quadratic equation $kx(x - 2) + 6 = 0$ has two real and equal roots.

   1. A.$0$ or $6$
   2. B.Only $6$
   3. C.$0$ or $-6$
   4. D.Only $-6$
   See the answer and solution
4. Question 4Q-517DFD

   Which of the following equations has the sum of its roots equal to $3$ and the product of its roots equal to $-10$?

   1. A.$x^2 - 3x - 10 = 0$
   2. B.$x^2 + 3x - 10 = 0$
   3. C.$x^2 - 3x + 10 = 0$
   4. D.$x^2 + 3x + 10 = 0$
   See the answer and solution
5. Question 5Q-77638C

   If $-5$ is a root of the quadratic equation $2x^2 + px - 15 = 0$ and the quadratic equation $p(x^2 + x) + k = 0$ has equal roots, find the value of $k$.

   1. A.$7$
   2. B.$-7$
   3. C.$\frac{7}{4}$
   4. D.$\frac{7}{2}$
   See the answer and solution