If the equations $a x^{2} + b x + c = 0$ and $x^{3} + 3 x^{2} + 3 x + 2 = 0$ have two common roots, then which one of the following is correct ?

a = 2 b = c

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

a = b = c

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

b^{2} = 4 a c

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

None of these

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

Open in App

Solution

The correct option is C $a = b = c$
$l e t r o o t s o f a x^{2} + b x + c = 0 b e, α & β a n d r o o t s o f x^{2} {+ 3 x}^{2} + 3 x + 2 = 0 b e, α, β & γ α β = \frac{c}{a} α β γ = - 2 γ = - \frac{2 a}{c} α + β = - \frac{b}{a} α + β + γ = - 3 γ = \frac{b}{a} - 3 γ = \frac{b - 3 a}{a} \frac{b - 3 a}{a} = - \frac{2 a}{c} b c - 3 a c = - 2 a^{2} 2 a^{2} - 3 a c + b c = 0 {2 a}^{2} = c (3 a - b) (A) i f a = 2 b = c {2 a}^{2} = a (6 b - b) 2 a \neq 5 b (B) i f a = b = c 2 a^{2} = a (2 a) {2 a}^{2} = 2 a^{2} (C) i f c = \frac{b^{2}}{4 a} 2 a^{2} \neq \frac{b^{2}}{4 a} (3 a - b)$

Suggest Corrections

Similar questions

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

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

If a,b,c $ϵ$ R and the equations a $x^{2} + b x + c = 0 a n d x^{3} + 3 x^{2} + 3 x + 2 = 0$ have two roots in common, then

x^{3} + 1 = 0

a x^{2} + b x + c = 0, a, b, c \in R

a + b

3 x^{2} - 2 \sqrt{6} x + 2 = 0

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

b^{2} - 4 a c > 0

b^{2} - 4 a c \geq 0

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

Join BYJU'S Learning Program