The question is about Finding the Roots of a bi-quadratic equation. Sum and product of the roots of the polynomial is given and we need to find out an algebraic expression of roots. Polynomials is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions. Clue: This question involves a particular rule from inequality.

Question 6: If x^{4} – 8x^{3} + ax^{2} – bx + 16 = 0 has positive real roots, find a – b.

- -8
- 6
- -12
- -14

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Let p, q, r, s be the roots of the equation

p + q + r + s = 8

pqrs = 16

This happens only when p = q = r = s = 2

\\frac{(p+q+r+s)}{4}\\) = 2.

√(pqrs) = 2.

Arithemtic mean is equal to Geometric Mean. This is possible only when all the numbers are equal. (Note that the question says all roots are positive and real)

p = q = r = s = 2

pq + pr + ps + qr + qs + rs = a

24 = a

pqr + pqs + prs+ qrs = b

32 = b

So, a – b = 24 – 32 = – 8

The question is **"If x ^{4} – 8x^{3} + ax^{2} – bx + 16 = 0 has positive real roots, find a – b."**

Choice A is the correct answer.

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