JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If equations \(ax^2 + bx + c = 0\) \(\left( {a,b,c \in R,a \ne 0} \right)\) and \(2x^2 + 3x + 4 = 0\) have a common root, then \(a : b : c\) equals
- A \(1 :2 : 3\)
- B \(2 :3 : 4\)
- C \(4 : 3 : 2\)
- D \(3 : 2 : 1\)
Answer & Solution
Correct Answer
(B) \(2 :3 : 4\)
Step-by-step Solution
Detailed explanation
Let \(\alpha, \beta\) be the common roots of both the equations. For first equation \(a x^{2}+b x+c=0\) we have \(\alpha+\beta=\frac{-b}{a}..........(1)\) \(\alpha . \beta=\frac{c}{a}..........(2)\) For second equation \(2 x^{2}+3 x+4=0\) we have…
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