If roots of equation {x^3} - 12{x^2} + 39x - 28 = 0 are in A.P. , then their common difference will

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8. Sequences and Series

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If the roots of the equation ${x^3} - 12{x^2} + 39x - 28 = 0$ are in $A.P.$, then their common difference will be

A

$ \pm 1$

B

$ \pm 2$

C

$ \pm 3$

D

$ \pm 4$

Solution

(c) 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 $(a – d)\,a\,(a + d) = 28$

==> $3a = 12$ and $a\,({a^2} – {d^2}) = 28$

==> $a = 4$ and $a\,({a^2} – {d^2}) = 28$

==> $16 – {d^2} = 7$

$\Rightarrow d = \pm \,3$.

Standard 11

Mathematics

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