• # question_answer If the roots of the equation ${{x}^{3}}-12{{x}^{2}}+39x-28=0$ are in A.P., then their common difference will be [UPSEAT 1994, 99, 2001; RPET 2001] A) $\pm 1$ B) $\pm 2$ C) $\pm 3$ D) $\pm 4$

Let a - d, a, a + d be the roots of the equation ${{x}^{3}}-12{{x}^{2}}+39x-28=0$ Then $(a-d)+a+(a+d)=12$ and $(a-d)\,a\,(a+d)=28$ Þ $3a=12$and $a\,({{a}^{2}}-{{d}^{2}})=28$ Þ $a=4$ and $a\,({{a}^{2}}-{{d}^{2}})=28$ Þ $16-{{d}^{2}}=7\Rightarrow d=\pm \,3$.