📢 Too many exams? Don’t know which one suits you best? Book Your Free Expert 👉 call Now!

    Question

    The roots of x² − (k+3)x + (3k − 1) = 0 are real

    and distinct, and the larger root exceeds the smaller by 5. Find k.
    A 2 ± √12 Correct Answer Incorrect Answer
    B 3 ± √21 Correct Answer Incorrect Answer
    C 5 ± √11 Correct Answer Incorrect Answer
    D 3 ± √29 Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let roots a, b with a − b = 5 and a + b = k+3, ab = 3k − 1. Then (a − b)² = (a + b)² − 4ab ⇒ 25 = (k+3)² − 4(3k − 1). ⇒ 25 = k² + 6k + 9 − 12k + 4 ⇒ 0 = k² − 6k − 12. k = [6 ± √(36 + 48)]/2 = [6 ± √84]/2 = [6 ± 2√21]/2 = 3 ± √21. Both make distinct real roots. Answer: k = 3 ± √21.

    Practice Next
    More Quadratic equation Questions
    ask-question