JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If the equations \({x^2} + 2x + 3 = 0\) and \(a{x^2} + bx + c = 0,a,b,c \in R\) have a common root ,then \(a:b:c = \) .. . .
- A \(1:2:3\)
- B \(3:2:1\)
- C \(1:3:2\)
- D \(3:1:2\)
Answer & Solution
Correct Answer
(A) \(1:2:3\)
Step-by-step Solution
Detailed explanation
\(x^{2}+2 x+3=0..........(i)\) \(a x^{2}+b x+c=0..........(ii)\) Since equation \((i)\) has imaginary roots So equation \((ii)\) will also have both roots same as \((i)\). Thus \(\frac{a}{1}=\frac{b}{2}=\frac{c}{3}\) \(\Rightarrow \quad a=\lambda, b=2 \lambda, c=3 \lambda\)…
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