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    Subject

    Quantitative Aptitude

    Topic

    Algebra

    A polynomial f(x) = x4– 11x3+ 31x2– 46x + 20 is defined. When it is divided by x2– 3x + n, the remainder left is q. Find the product of n and q.

    ক)
    20
    খ)
    30
    গ)
    40
    ঘ)
    50
    ঙ)
    100

    Explanation

    Let the quotient after division be x 2 + ax + b. ⇒ (x 2 – 3x + n)( x 2 + ax + b) + q = x 4 – 11x 3 + 31x 2 – 46x + 20 ⇒ x 4 + (a – 3)x 3 + (n – 3a + b)x 2 + (an – 3b)x + bn + q = x 4 – 11x 3 + 31x 2 – 46x + 20 Comparing, we get a = -8, n – 3a + b = 31, an – 3b = -46, bn + q = 20. Put value of a, we get n + b = 7, 8n + 3b = 46 Solving, we get n = 5, b = 2. Now, bn + q = 20 ⇒ q = 20 – 5× 2 = 10 ∴ Product of n and q will be 50.

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