If $x^{2} + 7 x + 1 = 0$ and $(a^{2} - 4 a) x + b x - 3 = 0$ have both the roots in common, then find the value of $a$ .

$4$

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

$3$

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

$1$

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

$2$

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

Open in App

Solution

The correct option is C
$1$

If two equations have the same roots or represent the same equation, then the ratio of the corresponding coefficients is same.
$x^{2} + 7 x + 1 = 0$ and $(a^{2} - 4 a) x + b x - 3 = 0$ represent the same equation.

$\Rightarrow$ We can compare the coefficients.

$\Rightarrow \frac{a^{2} - 4 a}{1} = \frac{b}{7} = \frac{- 3}{1}$

$\Rightarrow a^{2} - 4 a = - 3$

$\Rightarrow a^{2} - 4 a + 3 = 0$

$\Rightarrow (a - 3) (a - 1) = 0$

$\Rightarrow a = 1$ or $a = 3$

Suggest Corrections

Similar questions

x^{2} - 7 x + 10 = 0

x^{2} - 5 x + c = 0

c

If the equations $a x^{2} + b x + 1 = 0$ and $2 x^{2} + 4 x + 3 = 0$ have both the roots common, then the value of $a + b$ is:

x^{2} + a x + 10 = 0

x^{2} + b x - 10 = 0

a^{2} - b^{2}

If the equations $a x^{2} + b x + 1 = 0 a n d 2 x^{2} + 4 x + 3 = 0$ have both the roots common, then the value of a + b is

x^{2} + 3 x + 3 = 0

a x^{2} + b x + 1 = 0

a, b, \in, Q

(3 a + b)

Join BYJU'S Learning Program