Question

If x^4
- 8x^3+ ax^2 - bx + 16=0 has positive real roots,
find a b.​

Answer 1

Step-by-step explanation:

Note that (by using Vieta's Formula)

α1+α2+α3+α4=8

and

α1α2α3α4=16

Therefore AM=GM=2AM=GM=2

Deducing from AM−GM inequality (∑ni=1ain≥(∏ni=1ai)1/n), AM=GM only when all the terms are equal..Hence all roots are equal.AM−GM inequality (∑ni=1ain≥(∏ni=1ai)1/n), AM=GM only when all the terms are equal..Hence all roots are equal.

So α1=2 And x4−8x3+ax2−bx+16=(x−2)4α1=2 And x4−8x3+ax2−bx+16=(x−2)4

Multiply and compare coefficients.

So, (A) and (D) are true...(A) and (D) are true...

Hope that helps.