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

\pm 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\pm 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\pm 3

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\pm 4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

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

Suggest Corrections

Similar questions

x^{3} - 12 x^{2} + 39 x - 28 = 0

x^{3} - 12 x^{2} + 39 x - 28 = 0

x^{3} - 12 x^{2} + 39 x - 28 = 0

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

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

Join BYJU'S Learning Program