If the roots of $x^3-9x^2+23x-15=0$ are in A.P., then their common difference is …
🎥 Video solution / Text Solution of this question is given below:
Let roots be $a-d,\;a,\;a+d$. Then
sum $=3a=9 \Rightarrow a=3$.
Sum of pairwise products $=3a^2-d^2=23 \Rightarrow 27-d^2=23 \Rightarrow d^2=4$.
Hence $d=\pm2$.