Find the value of ' $a$ ' so that $x^{2} - 11 x + a = 0$ and $x^{2} - 14 x + 2 a = 0$ have a common root.

$12$

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

$24$

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

$0$

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

$48$

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

Open in App

Solution

The correct option is C
$0$

$x^{2} - 14 x + 2 a = 0$

$x^{2} - 11 x + a = 0$

Let the common root be $α$

$\frac{α^{2}}{- 14 a + 22 a} = \frac{- α}{a - 2 a} = \frac{1}{- 11 + 14}$

$\Rightarrow \frac{α^{2}}{8 a} = \frac{α}{a} = \frac{1}{3}$

$\Rightarrow \frac{α}{a} = \frac{1}{3}$
$\Rightarrow α = \frac{a}{3}$ ....... $(1)$

$\Rightarrow \frac{α^{2}}{8 a} = \frac{1}{3}$
$\Rightarrow α^{2} = \frac{8 a}{3}$

Using $(1)$
$\Rightarrow \frac{a^{2}}{9} = \frac{8 a}{3}$
$\Rightarrow \frac{a^{2}}{9} - \frac{8 a}{3} = 0$
$\Rightarrow$ $a^{2} - 24 a = 0$
$\Rightarrow a = 0$ or $24$

Suggest Corrections

Similar questions

x^{2} - 11 x + a = 0 and x^{2} - 14 x + 2 a = 0

x^{2} - 11 x + a = 0

x^{2} - 14 x + 2 a = 0

x^{2} - 11 x + a = 0

x^{2} - 14 x + 2 a = 0

a

x^{2} - 11 x + k = 0

x^{2} - 14 x + 2 k = 0

x^{2} - 11 x + a = 0

x^{2} - 14 x + 2 a = 0

a \neq 0,

Join BYJU'S Learning Program