CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations
For what value of k does the equation x^2 - (k + 2)x + 9 = 0 have equal roots, given that k is positive?
Setting the discriminant to zero gives (k+2) squared equal to 36, so k+2 is 6 or -6. Since k must be positive, k equals 4. The equation then becomes (x-3) squared, which has equal roots.
- A4Correct
- B6
- C8
- D10
Explanation
Equal roots need D = 0: (k+2)^2 - 36 = 0, so k + 2 = ±6. Thus k = 4 or k = -8; k positive gives k = 4. Choosing 6 comes from ignoring the +2 shift in the coefficient. Check: k=4 gives x^2 - 6x + 9 = (x-3)^2.
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