If and where have a common root, then the least value of a + b + c is

JEE MainMathematicsModerateQuadratic Equations

If $2x^{2} + 3x + 4 = 0$ and $ax^{2} + bx + c = 0$ where
$a,b,c \in N$ have a common root, then the least value of a + b + c is

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2x^{2} + 3x + 4 = 0

has imaginary roots. Thus the given
equations have identical roots.

\therefore\frac{a}{2} = \frac{b}{3} = \frac{c}{4} = k(say)

\Rightarrow a + b + c = 9k

for least value take k = 1

Source: Grass-G / M-16 Mathematics Paper 25 Nov First.docx

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