Multiple choice

If the difference between the roots of the equation x2 – 5x + 2k = 1 is 3, what is the value of k?

  1. 2

  2. 2.5

  3. 4

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

x^2 - 5x + (2k-1) = 0. Roots r1, r2. r1+r2 = 5, r1-r2 = 3. 2r1 = 8, r1 = 4. r2 = 1. Product r1*r2 = 4 = 2k-1. 2k = 5, k = 2.5.

AI explanation

Rewrite the given equation in the standard quadratic form to get x2 - 5x + (2k - 1) = 0. Using the relation between roots and coefficients, the difference of the roots is given by the square root of the discriminant divided by the coefficient of x2, which equals 3. Substituting the values gives ((25 - 4(2k - 1)) / 1) = 9, which simplifies to 29 - 8k = 9. Solving this linear equation yields 8k = 20, so k equals 2.5.

Keep practicing — related questions