Question

if alpha , beta and gamma are zeroes of 6x^3+3x^2-5x+1 , find the value of alpha^-1+beta^-1+gamma^-1.

Answer 1

Heya!!
____
Here given ,
⇒p(x)=6x³+3x²-5x+1

Here :a=6 ,b=3,c=-5 and d=1.

⇒α+β+Y=-b/a=-3/6=-1/2

⇒αβ+βY+Yα=c/a=-5/6

⇒αβY=-d/a=-1/6.

⇔To find :α^-1+β^-1+Y^-1

⇒we can write it : 1/α+1/β+1/Y

⇒βY+αY+αβ/αβY. Put the values

⇒-5/6/-1/6. : 6 gets cancelled

⇒5

Hope this helps you ☺☺