CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations
What are the roots of the equation x² − 9x + 20 = 0?
The roots are 4 and 5. The expression factorises as (x − 4)(x − 5), because 4 and 5 add up to 9 and multiply to 20. Setting each factor to zero gives x = 4 and x = 5.
- A4 and 5Correct
- B−4 and −5
- C2 and 10
- D−4 and 5
Explanation
Factorise: x² − 9x + 20 = (x − 4)(x − 5). So x = 4 or x = 5. Check: sum = 9 and product = 20. The option −4 and −5 would give a sum of −9, so it is wrong.
Did you get it right without looking?
One question tells you little. A timed set on Quadratic Equations shows your real accuracy, how long you take and where you lose marks.
More Quadratic Equations questions
- For the equation 2x^2 - 8x + k = 0, the roots are real and equal. What is the value of k?
- What are the roots of the equation x^2 - 9x + 20 = 0?
- The sum of the roots of 2x^2 - 11x + 14 = 0 is S and the larger root is L. What is the value of S + L?
- If α and β are the roots of 3x² − 6x + 2 = 0, what is the value of α² + β²?
- For which value of k does the equation x² − 6x + k = 0 have two equal roots?
- For which range of values of m does the equation x² + mx + 9 = 0 have no real roots?