# Polynomials

You are here: Home  CAT Questionbank   CAT Quant  Polynomials.  Question 6

## Finding the Roots

If x4 – 8x3 + ax2 – bx + 16 = 0 has positive real roots, find a – b.
1. -8
2. 6
3. -12
4. -14

Choice A. -8

Click to watch video solution

## Detailed Solution

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

## Our Online Course, Now on Google Playstore!

### Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.

### Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!