If equations ax2 + bx + c = 0, (a, b, c ∈ R, a ≠ 0) and 2x2 + 3x + 4 = 0 have a common root, then a: b: c equals :

Question

If equations ax2 + bx + c = 0, (a, b, c ∈ R, a ≠ 0) and 2x2 + 3x + 4 = 0 have a common root, then a: b: c equals : (A) 1: 2: 3 (B) 2: 3: 4 (C) 4: 3: 2 (D) 3: 2: 1

Tardigrade Admin · Accepted Answer

2x2+3x+4=0 as D le0 ⇒ both roots are imaginary ⇒ both roots arecommon ⇒ (a/2)=(b/3)=(c/4)

Q. If equations $a x^{2} + b x + c = 0, (a, b, c \in R, a \neq = 0)$ and $2 x^{2} + 3 x + 4 = 0$ have a common root, then $a : b : c$ equals :

1 : 2 : 3

2 : 3 : 4

4 : 3 : 2

3 : 2 : 1

$2 x^{2} + 3 x + 4 = 0$ as $D \leq 0$
$\Rightarrow$ both roots are imaginary
$\Rightarrow$ both roots arecommon
$\Rightarrow \frac{a}{2} = \frac{b}{3} = \frac{c}{4}$

Q. If equations ax2+bx+c=0,(a,b,c∈R,a=0) and 2x2+3x+4=0 have a common root, then a:b:c equals :