If the roots of the equation $x^{2} + a x + b = 0$ are $c$ and $d$ , then one of the roots of equation $x^{2} + (2 c + a) x + c^{2} + a c + b = 0$ is

$c$

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

$2 c$

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

$d - c$

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

$2 d$

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

Open in App

Solution

The correct option is C
$d - c$

Given equation: $x^{2} + a x + b = 0$

Roots are: $c$ and $d$

$c + d = - a$ and $c d = b$

$\Rightarrow c^{2} + a c + b = 0$ . . . $(1)$

$x^{2} + (2 c + a) x + c^{2} + a c + b = 0$

Using equation $(1)$ ,

$\Rightarrow x^{2} + (2 c + a) x = 0$

$\Rightarrow x [x + (2 c + a)] = 0$

$\Rightarrow x = - 2 c - a = - 2 c + c + d = d - c$

Suggest Corrections

Similar questions

If the roots of the equation $x^{2} + a x + b = 0$ are c & d, then one of the roots of equation $x^{2}$ + (2c + a)x + $c^{2}$ + ac + b = 0 is

If the roots of the equation $x^{2} + a x + b = 0 a r e c & d$ , then one of the roots of equation $x^{2} + (2 c + a) x + c^{2} + a c + b = 0$ is

If the roots of the equation $x^{2} + a x + b = 0$ are $c$ and $d$ , then one of the roots of equation $x^{2} + (2 c + a) x + c^{2} + a c + b = 0$ is

8, 2

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

3, 3

x^{2} + d x + b = 0

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

Join BYJU'S Learning Program