Question

If $\alpha ,\beta ,\gamma$ are the roots of $x^3-3x^2+4x-7=0$, then $(\alpha +2)(\beta +2)(\gamma +2)=$

• A. $25$
• B. $-25$
• C. $35$
• D. $-35$

Answer 1

Answer: (C)

$35$

As $\alpha ,\beta ,\gamma$ are roots of $x^3-3x^2+4x-7=0$
Replace $x\to x-2$ in equation, we get
${(x-2)}^3-3{(x-2)}^2+4(x-2)-7=0\Rightarrow x^3-9x^2+3-x-35=0$

And roots this equations are $(\alpha +2),(\beta +2),(\gamma +2)$

Then, product of roots $=(\alpha +2)(\beta +2)(\gamma +2)=-(-35)=35$