CA Foundation · Quantitative Aptitude · Equations
If the sum of the roots of the equation 2x² − (k + 1)x + 8 = 0 is equal to the product of its roots, what is the value of k?
The value of k is 7. The sum of roots is (k + 1)/2 and the product is 8/2 = 4. Equating them gives k + 1 = 8, so k = 7, and the resulting equation 2x² − 8x + 8 = 0 has sum and product both 4.
- A7Correct
- B3
- C−5
- D8
Explanation
Sum = (k + 1)/2 and product = 8/2 = 4. Setting (k + 1)/2 = 4 gives k + 1 = 8, so k = 7. Check: 2x² − 8x + 8 = 0 has sum 4 and product 4. Option 3 results from wrongly using product 8/… and forgetting the factor, taking k + 1 = 4.
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