CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations
For the equation 2x² − 5x + k = 0 to have equal roots, what must be the value of k?
The value of k is 25/8. Equal roots require the discriminant to be zero, so 25 − 4×2×k = 0, which gives 8k = 25. Hence k = 25/8. Using only 4k instead of 8k would wrongly give 25/4.
- A25/8Correct
- B5/4
- C25/4
- D8/25
Explanation
Equal roots need discriminant zero: b² − 4ac = 25 − 8k = 0, so k = 25/8. The value 25/4 comes from using 4ac as 4k instead of 8k, which is the wrong product.
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 which value of k does the equation x² − 6x + k = 0 have two equal roots?
- A firm's break-even output x (in units) satisfies x² − 70x + 1000 = 0. What is the product of the two break-even outputs, and what is their …
- For the quadratic equation 2x^2 - 5x + 3 = 0, the discriminant and the nature of its roots are:
- If one root of x^2 - 9x + k = 0 is twice the other root, what is the value of k?
- A rectangular plot belonging to Sharma Traders has a perimeter of 70 m and an area of 300 m². What is the length of the longer side?
- A rectangular plot of Mehta Traders has length 5 m more than its breadth, and its area is 266 square metres. What is the length of the plot?