Question

When each root of the equation \[ x^3-ax^2+bx+1=0 \] is diminished by \(h\), if the transformed equation takes the form \[ 9x^3+\left(9+\frac{a^3}{3}\right)=0, \] then \(ah=\)

• A. \(b\)
• B. \(1\)
• C. \(a^2+b\)
• D. \(\dfrac{b^2}{3}\)

Hint:

If every root of a polynomial is decreased by \(h\), replace \[ \boxed{x\rightarrow x+h.} \] After expansion, compare coefficients to determine the required value.

Answer 1

The Correct Option is A