Polynomials

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Cubic Equation

    x3 – 4x2 + mx – 2 = 0 has 3 positive roots, two of which are p and . Find m.
    1. 5
    2. -11
    3. 8
    4. -2

 

  • Correct Answer
    Choice A. 5

Explanatory Answer

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Detailed Solution

Let the roots be p, and q.

So, the 3rd root = q = 2
p + + 2 = 4
p + = 2 {For any real p |p + | }
p2 – 2p + 1 = 0
(p – 1)2 = 0. Hence, p is 1.
The roots are 1, 1 and 2.
(1 × 1) + (1 × 2) + (1 × 2) = 5 = m
Answer choice (a)



Correct Answer: 5.



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