Question

If the roots of $x^3-12x^2+39x-28=0$ are in AP then their common difference is

• A. $\pm 1$
• B. $\pm 2$
• C. $\pm 3$
• D. $\pm 4$

Answer 1

Answer: (C)

$\pm 3$

Let $a-d,a,a+d$ are roots of $x^3-12x^2+39x-28=0$ as roots are in A.P
Then
$s_1=3a=12\Rightarrow a=4s_3=a(a^2-d^2)=28\Rightarrow 16-d^2=\frac{28}{4}\Rightarrow d^2=16-7=9\Rightarrow d=\pm 3$